This has been CNBC's live blog covering updates on the war in Ukraine. [Follow the latest updates here.]

Face-to-face talks between Ukraine and Russia are set to continue this week, with delegations from both countries traveling to Turkey today.

Kremlin spokesperson Dmitry Peskov told reporters that discussions were likely to resume Tuesday.

Meanwhile, Ukrainian officials said they would not be opening any humanitarian corridors Monday to allow the evacuation of civilians due to intelligence that suggested Russian forces may be planning an attack on the evacuation routes.

Ukrainian counterattacks have pushed Russians back from a number of positions, Britain says

The U.K. Ministry of Defence said Ukrainian forces have pushed Russian troops back in some locations as they conduct counterattacks northwest of Kyiv.

Still, the ministry said in its daily update that "Russia still poses a significant threat to the city through their strike capability."

While Russian forces have continued their onslaught in Mariupol, the ministry said the city center remains under Ukrainian control.

Military developments are difficult or impossible to confirm as the situation on the ground in Ukraine changes rapidly.

Reports of Ukrainian units reclaiming territory north and west of Kyiv began to filter out of the region last week.

— Christine Wang

Japan to ban luxury exports to Russia starting April 5

Japan is expected to ban the export of luxury products such as passenger cars and fashion items to Russia starting April 5, according to the Ministry of Economy, Trade and Industry.

Banned items include: alcohol, tobacco products, perfume, cosmetics, motorcycles, watches with precious metals, art and antique goods, the ministry said in a Tuesday statement translated by NBC News.

The move is the latest response from Japan aimed at putting pressure on Russia for its unprovoked war against Ukraine.

— Sumathi Bala

Ukrainians claim to retake ground ahead of latest talks

Ukrainian forces claimed to have retaken a Kyiv suburb and an eastern town from the Russians in what is becoming a back-and-forth stalemate on the ground, while negotiators began assembling for another round of talks Tuesday aimed at stopping the fighting.

Ahead of the talks, to be held in Istanbul, Ukrainian President Volodymyr Zelenskyy said his country is prepared to declare its neutrality, as Moscow has demanded, and is open to compromise on the fate of the Donbas, the contested region in the country's east.

The mayor of Irpin, a northwestern Kyiv suburb that has been the scene of some of the heaviest fighting near the capital, said Monday that the city has been "liberated" from Russian troops.

Irpin gained wide attention after photos circulated of a mother and her two children who were killed by shelling as they tried to flee, their bodies lying on the pavement with luggage and a pet carrier nearby.

— Associated Press

Biden says his 'moral outrage' at Putin does not signal a U.S. policy shift

President Joe Biden on Monday clarified that his statement that Russian President Vladimir Putin "cannot remain in power" made over the weekend doesn't reflect a policy shift by the United States.

Biden spoke at the White House two days after he shocked the world and his closest aides on Saturday when he ad-libbed the line during a major speech in Poland, prompting a flurry of headlines saying Biden was calling for a regime change in Russia.

On Monday, Biden tried to draw a line between her personal opinion and U.S. policy.

"I'm not walking anything back," said Biden. "I was expressing the moral outrage I felt" after having visited with Ukrainian refugees.

"I was not then, nor am I now, articulating a policy change," he added.

— Christina Wilkie

Nuclear material at Kharkiv research site is undamaged after renewed shelling

A nuclear research facility in the war-torn city of Kharkiv in northeast Ukraine has been damaged, but the nuclear material within it remains unharmed, International Atomic Energy Agency Director General Rafael Mariano Grossi said.

The facility, which contains only a small amount of nuclear material, had already been attacked earlier in March as Russian forces blitzed Kharkiv.

Ukraine told the IAEA on Saturday that the site had come under additional fire, according to a press release from the agency.

In an update Monday, the IAEA said "the building, its thermal insulation and the experimental hall were damaged," but the nuclear material-containing neutron source "was not."

The facility "has been used for  research and development and radioisotope production for medical and industrial applications," the IAEA said, adding that its nuclear material "is subcritical – there can be no nuclear chain reaction – and the radioactive inventory is low."

— Kevin Breuninger

Ukrainians race to protect their national monuments

Ukrainians race to protect their national monuments and statues from Russian shelling.

— Getty Images

Biden's budget proposal would send more defense assistance to Ukraine

U.S. President Joe Biden's 2023 budget proposal would direct even more money toward Ukraine's defense against Russia's invasion.

The White House called for an $813 billion defense budget, including $31 billion in new spending. The Biden administration said a chunk of the total, $6.9 billion, would go to NATO, European defense, Ukraine and countering Russian aggression.

The budget request expresses Biden's priorities but does not set policy. Congress ultimately proposes and approves federal spending.

— Christina Wilkie

Negotiations with Ukraine moving forward, Russia’s Lavrov claims

Negotiations with Ukraine are moving forward with some difficulty, Russian Foreign Minister Sergey Lavrov said in an interview on Monday.

Speaking with a Serbian television channel, Lavrov claimed Ukraine's delegation "keeps going back on its own suggestions" during talks with Russia, but he added that the negotiations "are moving forward."

Delegates from Russia and Ukraine are traveling to Turkey today for a fresh round of face-to-face talks.

"Negotiations will continue tomorrow in person, but we still don't have a clear understanding on our main points," Lavrov said Monday, according to an NBC News translation.

He said these were the demilitarization and what Russia has called the "denazification" of Ukraine — a claim repeatedly laid out by Moscow as a justification for its invasion, and one widely rubbished by the international community.   

Lavrov also said in Monday's interview that Russia still has "a lot of allies, including Latin American, South-East Asian and African countries." 

"The West will keep enforcing sanctions on Russia no matter what, because it's purpose is not to solve any particular problem, but to stop Russian progress and development," Lavrov claimed.

— Chloe Taylor

Kremlin says it’s monitoring Biden’s comments on Putin

U.S. President Joe Biden's remarks that his Russian counterpart "cannot remain in power" are alarming, the Kremlin said Monday.

"Well, this is a statement that is certainly alarming," Kremlin spokesperson Dmitry Peskov said at a press briefing. "We will continue to closely monitor the statements of the U.S. president. We are carefully recording them — and we will continue to do so."

Biden said during a speech in Poland on Saturday that Putin "cannot remain in power," referring to the Russian president as "a dictator" who was "bent on rebuilding an empire."

The White House later walked back Biden's comments, saying the Biden administration was not calling for regime change in Russia and that the president had been referring to Putin attempting to exert power over the European continent.

— Chloe Taylor

Heineken says it’s leaving Russia

Drinks giant Heineken has announced it will leave the Russian market.

"We have concluded that Heineken's ownership of the business in Russia is no longer sustainable nor viable in the current environment. As a result, we have decided to leave Russia," the company said in a statement on Monday.

Heineken had earlier announced that it would stop new investments and exports to Russia as well as ending the production, sale and advertising of the Heineken brand in the country. It also said it would not accept any profit from its business in the country.

"We aim for an orderly transfer of our business to a new owner in full compliance with international and local laws," the company added on Monday. "To ensure the ongoing safety and wellbeing of our employees and to minimize the risk of nationalization, we concluded that it is essential that we continue with the recently reduced operations during this transition period."

Heineken would pay the salaries of its 1,800 Russian employees until the end of this year, and would not profit from the transfer of ownership of its business in Russia, the company said.

— Chloe Taylor

Ukraine says Russian forces trying to capture Kyiv’s key roads and settlements

Ukraine's Ministry of Defense has said that fighting is ongoing in several regions, with several cities — including Kyiv — "restraining the advance of the Russian enemy."

"The grouping of Ukrainian forces and means of defense of the city of Kyiv is deterring the Russian enemy, which is trying to break through the Ukrainian defense from the northwest and east in order to take control of key roads and settlements," the ministry said in an update.

Russian forces are also advancing on the settlements of Huliaipole, Zaporizhzhia and Verkhnotoretske, as well as cities in southern Ukraine, officials said.

— Chloe Taylor

Kremlin says negotiations are unlikely to resume before Tuesday

Kremlin spokesperson Dmitry Peskov has told reporters that delegations from Russia and Ukraine are flying to Turkey today, with face-to-face negotiations likely to begin tomorrow.

"[Negotiations] are unlikely to continue today. Today, delegations are indeed going to Turkey. So, we know that this [talks] could theoretically happen tomorrow," he said during a press briefing.

"We cannot and will not talk about progress yet. But the very fact that it was decided to continue the talks in person is certainly important. But for now, we still adhere to the line of non-disclosure of any details related to the negotiations."

David Arakhamia, a Ukrainian official who has been taking part in negotiations with Russia, said on Sunday that delegates had decided to hold this round of talks in-person between Monday and Wednesday this week.

— Chloe Taylor

Officials say there were no attacks on Ukrainian capital overnight

The Kyiv City Administration said Monday that Ukraine's capital was "calm" overnight, and that there had been no attacks on the city.

Officials said in a Telegram post that Kyiv's infrastructure was working, and citizens were being provided with all utilities.

They also urged residents of the capital not to leave their homes unnecessarily.

— Chloe Taylor

Ukrainian official not expecting a major breakthrough at this week’s talks with Russia

Vadym Denysenko, an advisor to the Ukrainian Interior Ministry, has said that he does not expect any major breakthroughs during this week's talks between Russian and Ukrainian officials.

Delegations from both countries are set to meet in Turkey on Monday for face-to-face talks, which are expected to run until Wednesday.

Denysenko was speaking during a charity "television marathon," shown around the world, in support of Ukraine.

— Chloe Taylor

Ukraine won’t open humanitarian corridors Monday over fear of ‘provocations’

Ukrainian Deputy Prime Minister Iryna Vereshchuk has said that authorities will not be opening humanitarian corridors today, as officials fear a Russian attack is looming.

"Our intelligence reported possible provocations by the occupiers on the routes of humanitarian corridors," she said on messenger app Telegram. "Therefore, for reasons of public safety, we do not open humanitarian corridors today."

Ukrainian officials have operated safe exit routes in various locations across the country on an almost daily basis in recent weeks, with the corridors enabling the evacuation of civilians and the import of vital supplies.

Early attempts to evacuate civilians from the cities of Mariupol and Volnovakha had to be halted, as Ukrainian authorities said Russian forces were violating cease-fire agreements along the evacuation routes.

— Chloe Taylor

Ukraine says 143 children have been killed in the war

The office of Ukraine's attorney general said Monday that 143 children have been killed in Ukraine since Russia's invasion began on Feb. 24.

A further 216 children had been wounded in the war, officials added.

Children in Kyiv, Kharkiv and Donetsk "suffered the most," the attorney general's office said, but noted that children had been badly affected across 14 regions of Ukraine.

— Chloe Taylor

Russia and Ukraine delegates to meet in Turkey for talks

Delegations from Ukraine and Russia are scheduled to meet in Turkey today to conduct more talks.

David Arakhamia, a Ukrainian official who has been taking part in negotiations with Russia, said in a Facebook post on Sunday that delegates had decided to hold this round of talks in-person.

"Today, at the next round of talks on video connection, it was decided to hold the next live round by two delegations in Turkey on March 28-30," he said, according to an NBC News translation.

— Chloe Taylor

Ukrainian officials reportedly say Russian forces are withdrawing from some locations

The Mayor of Slavutych — home to employees of the Chernobyl nuclear power plant — said Monday that Russian troops have left the town, Reuters reported.

"They completed the work they had set out to do," Mayor Yuri Fomichev said in an online video post, according to the news agency. "They surveyed the town, today they finished doing it and left the town. There aren't any in the town right now."

On Saturday, Ukrainian media reported that Slavutych had been captured by Russian forces.

Meanwhile, Ukraine's armed forces said in the early hours of Monday morning that some Russian troops were withdrawing from the Kyiv region to Belarus.

"The regrouping of individual units from the composition of the [Russian] Eastern Military District continues," the armed forces said in a Facebook update.

"Units that have suffered significant losses in the process of offensive actions are usually taken to the territory of Belarus for the restoration of militia," the update added, saying the withdrawal from the territory of the Kyiv region was "celebrated."

But officials noted that battles continued across the country, and that Russian forces "continue missile and aviation strikes on important military infrastructure and advanced positions aimed at causing losses and personnel exhaustion."

CNBC has not been able to independently verify these reports.

— Chloe Taylor

Russia will likely launch cyberattacks on oil and gas infrastructure, warns cybersecurity firm

Russian cyberattacks on oil and gas infrastructure are highly likely given the country's history of "tit-for-tat" action against sanctions, said Rob Lee, co-founder and CEO of cybersecurity firm Dragos.

"In 2014 when Russia invaded Ukraine and took Crimea, there was a number of … sanctions levied from the Western financial institutions," Lee said on CNBC's "Street Sign Asia."

"As a result, Russia ended up using cyberattacks back against those financial institutions."

"Now that we're seeing sanctions against oil and gas infrastructure, Nord Stream 2 etc … we absolutely expect to start seeing cyberattacks against oil and gas infrastructure," he said. Germany halted the certification of the Nord Stream 2 in late February — the gas pipeline was designed to bring natural gas from Russia directly to Europe.

Such an attack could have an "oversized impact" even if the disruption is not big, due to the high connectivity of the global oil and gas sector, Lee said, citing how a recent attack by Yemen's Houthis on a Saudi Aramco facility resulted in oil prices jumping.

"I think it's really incumbent on these industries to try to be proactive," he said.

U.S. President Joe Biden has warned U.S. corporations to strengthen their cybersecurity practices in light of intelligence reports indicating Russia is looking at potential attacks.

— Eustance Huang

‘No significant change to Russian forces' dispositions,’ UK says

The U.K.'s Ministry of Defense has said that over the last 24 hours there have been "no significant change to Russian forces' dispositions in occupied Ukraine."

A continued lack of momentum and morale among the Russian military, as well as ongoing logistical shortages and aggressive resistance from the Ukrainians are all causing problems for Russia, the U.K. said in an intelligence update.

"Russia has gained most ground in the south in the vicinity of Mariupol where heavy fighting continues as Russia attempts to capture the port," it added.

— Chloe Taylor

Read CNBC’s previous live coverage here:

You can read Sunday's live coverage of the war in Ukraine here:

Zelenskyy says Ukraine ready to discuss neutrality status; Blinken says U.S. not seeking regime change

India is buying up cheap Russian oil at 'record discounts' and China may follow suit

Russia's crude oil deliveries to India were fairly infrequent last year, but there's been a "significant uptick" since the Russia-Ukraine war began, say industry observers.

Russian crude is being sold at "record discounts," says the International Energy Agency.

Ellen Wald, president of Transversal Consulting, said a couple of commodity trading firms were also offering discounts of up to $30 per barrel two weeks ago for the Urals blend — the main oil blend that Russia exports.

While India's motivations are economic, it would also likely weigh its friendship with Russia in purchasing its oil — since both countries having a long history, said Samir N. Kapadia, head of trade at government relations consulting firm Vogel Group.

Analysts say China, the largest oil importer in the world, could also go for discounted oil from Russia. "China really would prefer much cheaper oil … prices are way too high even in the $90 range that's too high for China," said Ellen Wald, president of Transversal Consulting.

— Weizhen Tan

Zelenskyy says Ukraine ready to discuss neutrality status

Ukrainian President Volodymyr Zelenskyy said his country is prepared to discuss adopting a neutral status as part of a peace deal with Russia, though an agreement would need to be guaranteed by third parties and put to a referendum.

"Security guarantees and neutrality, non-nuclear status of our state. We are ready to go for it. This is the most important point," Zelenskyy said in a 90-minute video address with Russian journalists.

Zelenskyy said that while his government is discussing the use of the Russian language in Ukraine in its talks with Russia, other Russian demands such as demilitarization are not currently on the table. He said Russian-speaking cities in Ukraine have been destroyed during the invasion.

— Ian Thomas, with reporting from Reuters