The Federal Deposit Insurance Corporation is leading an auction to find a potential buyer for Silicon Valley Bank after the US government said it would help depositors in its efforts to stop contagion across the banking sector.

Initial bidding closed at 2pm Eastern Time, according to people familiar with the matter, although the deadline could be extended if necessary.

The search for a buyer comes as Janet Yellen assured US customers of the failed tech lender, which was taken over by the FDIC on Friday, that policies were being discussed to ensure depositors have access to their funds, despite dismissing the idea of a bailout.

“Let me be clear that, during the financial crisis, there were investors and owners of systemic large banks that were bailed out . . . and the reforms that have been put in place means we are not going to do that again,” Yellen said on Face the Nation. “But we are concerned about depositors, and we’re focused on trying to meet their needs.”

The FDIC has previously said SVB customers whose accounts were insured will have access to their funds on Monday. However, most of the lender’s customer are uninsured, prompting some this weekend to rush to sell their deposits to pay salaries and other operating expenses. At the end of last year, almost 96 per cent were not covered by the FDIC insurance policy, which guarantees deposits up to $250,000. The FDIC said it would pay uninsured customers an “advance dividend” within the week which would be a percentage of their deposits.

Yellen’s intervention comes amid calls from investors, entrepreneurs and some lawmakers for the government to step in more forcefully to ensure all depositors are made whole, or risk other banks coming under pressure as customers rush to stash cash in larger institutions.

“We must make sure all deposits exceeding the FDIC $250K limit are honoured. Banking is about confidence,” Eric Swalwell, a Democratic congressman from California wrote on Twitter. “If depositors lose confidence on the safety of their deposits over 250k then we are in trouble.”

Mitt Romney, the Republican senator from Utah, said depositors should “recover and have access to their deposits in order to meet their payrolls, pay their suppliers, and to prevent contagion”.

Andrew Yang, an entrepreneur and former Democratic presidential candidate, warned that “thousands of companies will fold or lay people off next week because of lack of access to accounts through no fault of their own”, imploring the Treasury or the state of California to intervene.

Billionaire hedge fund investor Bill Ackman issued one of the most urgent calls on Saturday, warning of a run on all but the biggest banks should the government stop short of guaranteeing all of SVB’s deposits or should the lender not be acquired by JPMorgan, Citigroup or Bank of America.

“The unintended consequences of the [government’s] failure to guarantee SVB deposits are vast and profound and need to be considered and addressed before Monday. Otherwise, watch out below,” he wrote on Twitter.

Other lawmakers voiced their opposition to a bailout, however, suggesting little consensus about the path forward.

Speaking on Meet the Press on Sunday, senator Bob Menendez, a Democrat, said: “I’m not ready to offer them a bailout by any stretch of the imagination.”

Mark Warner, the Democratic senator from Virginia, meanwhile, said that questions about “moral hazard” also must be considered.

The Treasury secretary on Sunday said she had been “working all weekend” with banking regulators to “design appropriate policies to address this situation”, adding that the FDIC was considering a “wide range of available options”, which included acquisitions.

Asked about the potential for broad-based contagion, Yellen affirmed that the banking system was “really safe and well-capitalised”, as well as “resilient”.

“Americans need to feel confident that the banking system is safe and sound, that it can meet the credit needs of households and businesses, and that depositors don’t have to worry about losing access to their money,” she said.