• Silicon Valley Bank's new CEO Tim Mayopoulos pitched venture and startup clients hard to help keep the bank alive in a 30-minute call.
• Mayopoulos said all options remain on the table for the future of the bank, and that there's no clear timetable on next steps.
• The CEO implored venture clients to bring funds back to the bank, noting that if they did so, the firm would try to forego pursuing any violations of exclusivity clauses.

Three days into his tenure as Silicon Valley Bank's government-appointed CEO, Tim Mayopoulos has a message for his high-powered venture capital and startup clients: Bring your money back.

That was consistent throughout Mayopoulos' responses as he fielded over 400 questions from concerned clients on a 30-minute Zoom call Wednesday.

"There is no safer place in the U.S. banking system to put your deposits," Mayopoulos said on the call, which CNBC attended and was first to report. He urged clients to return their funds to the bank and to promptly alert their relationship teams of any issues with inbound or outbound wire transfers, a point of concern for many corporate executives who were unable to pull their deposits from the bank last week.

Mayopoulos was joined by SVB operating chief Phil Cox, the only remaining executive from the core C-suite team. SVB's former CEO and CFO are no longer employed by the bank, Mayopoulos said on the call.

While Mayopoulos is making his pleas to current and former clients, it's not clear how long he will stay in his current job as the bank is currently controlled by the Federal Deposit Insurance Corporation. Mayopoulos said he doesn't know what SVB's "exact end state" would look like, and he listed three possibilities: recapitalization, sale, or liquidation.

A recapitalization would allow SVB to continue to exist as a standalone entity. But that possibility depends on another financial institution or group of investors stepping up.

"I recognize I'm new on the scene," Mayopoulos said in direct response to concerns from venture capital firms. "You've been patient with us as we've gone through some of those operational difficulties. All I would ask is give us a chance to win back your trust and confidence."

Mayopoulos' pitch was tailored towards the venture investors that have taken to social media in droves to express shock and dismay at the collapse of a storied Silicon Valley institution. On the call, Mayopoulos repeatedly referred to the "innovation economy," and to a startup ecosystem in which "Silicon Valley has played an important part."

Customer feedback will be critical in determining the future of the bank, Mayopoulos said on the call. Input "from clients and from the venture capital and entrepreneurial community" would shape the timetable for SVB's ultimate emergence from government control.

"One of the things I want to convey to you is that you have some agency in this that you actually get to vote, at least to send clear signals about what you want the outcome of this process to be," the CEO said in his prepared remarks. "If our clients choose to take their deposits and keep them in other institutions, that clearly limits the range of options that we have in terms of the ultimate outcome."

SVB's longstanding relationship with Silicon Valley's most elite venture firms is mutually beneficial and symbiotic.

From its founding at a poker table until the nearly fatal bank run last week, SVB was focused on taking risks in a market that most traditional banks shunned. SVB found a niche in venture debt, funding companies that needed cash infusions, especially between funding rounds.

In exchange for future consideration, often equity or warrants in a company, SVB became a mammoth player in the venture debt space, extending from software and internet into life sciences and robotics.

In its over 40 of business, SVB grew along with its depositors, building out a lucrative mortgage business and a suite of private-banking products that allowed it to retain and charm the founders whose fortunes the bank helped create.

From legacy enterprises like Cisco to more modern tech companies such as DocuSign and Roku, SVB has focused on providing financing and banking services at every stage of growth.

"There are other places that do venture debt, but Silicon Valley Bank was the 1,000-pound gorilla in the room," said Ami Kassar, CEO of the business lending consultant Multifunding.

Exclusivity contracts, meaning an ironclad promise that a company would keep all its money at SVB, were a key facet of those funding deals. When SVB failed, it roiled startups that had traded banking flexibility for liquidity. Some fled the bank, violating their covenants to keep their lights on and their payroll checks rolling.

When asked about potential exclusivity violations, Mayopoulos indicated that he understood emergency actions taken by startups.

"Given the change in circumstances and what the FDIC has done around insurance coverage, we'd very much like to work with our clients to have those deposits come back to us," the CEO said on the call.

Clients who return wouldn't have to worry about any fallout from breach of their covenants, Mayopoulos suggested. He didn't say what would happen to ex-customers who did the same.

— CNBC's Cat Clifford contributed to this report.