• Indoor family entertainment centers, such as arcades, trampoline parks and laser tag facilities, will be allowed to reopen in New York state starting March 26 at 25% capacity.
• Outdoor amusement parks will be allowed to return in April, and summer camps can resume in June, Gov. Andrew Cuomo said.
• They'll have to adhere to additional precautions, such as social distancing, mask wearing and frequent cleaning, he said.
• Cuomo and federal health officials are concerned, however, that highly contagious variants of the virus could threaten the nation's progress.

New York is forging ahead with reopening more businesses amid a post-holiday decline in Covid-19 cases, but the governor said the state is keeping "one eye" on troublesome variants of the virus that could reverse its progress.

Indoor family entertainment centers, such as arcades, trampoline parks and laser tag facilities, will be allowed to reopen starting March 26 at 25% capacity with additional precautions, such as social distancing, mask wearing and frequent cleaning, Gov. Andrew Cuomo said Wednesday.

Outdoor amusement parks can reopen on April 9 at 33% capacity with similar requirements, and parents can plan for overnight summer camps to return at some point in June, the Democratic governor said on a call with reporters.

"That doesn't happen until June," Cuomo said regarding summer camps, "and we hope the current trajectory stays until June — one eye on these variants of interest. But they can plan on reopening."

The governor has gradually started to lift more restrictions on businesses in recent weeks as the state rolls out more doses of Covid vaccines and cases continue to decline from a post-holiday surge.

The state is reporting a weekly average of 7,949 Covid cases per day, a more than 8% decline compared with a week ago and the lowest figure since the beginning of December, according to a CNBC analysis of data compiled by Johns Hopkins University.

Last week, Cuomo said large stadiums and arenas in New York will reopen at the end of February with required testing beforehand, a strategy where the state "wants to lead the way." Over the weekend, New York City restaurants were allowed to reopen their indoor dining sections at 25% capacity.

However, new and highly contagious Covid-19 variants could reverse New York's progress or hinder its planned reopenings. The governor said the state has now identified 82 Covid-19 cases with the variant first identified in the United Kingdom in December, known as B.1.1.7, with 12 cases added since Saturday. He said most of those new cases were found in the New York City area.

Federal health officials have repeatedly asked Americans to keep their guard up in the midst of the highly contagious variants first found in the United Kingdom, South Africa and Brazil.

So far, the U.S. has identified at least 1,277 Covid-19 cases with the B.1.1.7 variant, 19 of the B.1.351 variant, which was discovered in South Africa, and 3 cases of the P.1 variant, found in Brazil, according to recent data from the CDC.

"I think we should be assuming that the next wave of case growth, to the extent that we have it, is going to be with B.1.1.7, and that's something that I think everybody has to be even more cautious about," Andy Slavitt, a White House Covid senior advisor, told MSNBC on Monday.

Dr. Rochelle Walensky, head of the U.S. Centers for Disease Control and Prevention, said Wednesday that nationwide Covid cases have declined for five consecutive weeks, and new hospitalizations have similarly dropped since early January.

However, the spread of coronavirus variants that are more transmissible "could jeopardize the progress we have made in the last month if we let our guard down," Walensky said during a White House Covid response team press briefing.