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First Republic Bank's financial woes appeared to be deepening despite an industry-led emergency cash infusion.

The beleaguered bank is trying to raise money through a private issue of new shares, according to the New York Times, which cited people familiar with the situation.

The news comes just 24 hours after First Republic secured a cash infusion of $30 billion from a consortium of banks.

A full sale of the bank remains on the table, according to one of the people who spoke to the Times.

First Republic declined to comment to CNN.

Stocks fell Friday, ending the day lower as tumult in the banking sector continued to unnerve Wall Street.

The Dow ended the week down 1.2%. The S&P 500 ended the week up 1.4%. The Nasdaq Composite rose 4.4%.

Shares of First Republic continued their plunge and were down about 33%, even after a group of large banks intervened to offer the troubled bank $30 billion in deposits.

Credit Suisse stock slipped about 8% as Wall Street remained concerned about the bank's ability to recover from this week's turmoil.

Investors are hoping next week's Federal Reserve meeting will shed more light on the trajectory of the economy following a troublesome week. Traders see a roughly 63% probability for a quarter-point hike, according to the CME FedWatch Tool.

The Dow tumbled roughly 385 points, or 1.2%.

The S&P 500 fell 1.1%.

The Nasdaq Composite slipped 0.7%.

Regional bank Western Alliance said business is pretty much back to normal after concerns about Silicon Valley Bank's collapse sent shockwaves through the banking sector.

Western Alliance has $20 billion of cash on hand and the amount of withdrawals from accounts has plunged in recent days. The bank said it has a "significant" amount of money coming in from deposits, and a large number of new accounts were opened.

That's a sharp contrast from Monday, when customers had been yanking deposits out of the bank in fear that Western Alliance may be the next bank to fail. Other regional banks, including First Republic and PacWest, have also struggled mightily to reassure customers and investors that they're healthy.

Still, Western Alliance's stock fell 15% Friday.

The bank said as of yesterday, 55% of its deposits were insured. That compares to just 7% at SVB, where many tech companies stored millions of dollars of cash — well in excess of the FDIC's $250,000-per-account insurance limit. In an extraordinary action Sunday, the FDIC guaranteed all Silicon Valley Bank customers' deposits.

“We have a long history of financial stability and responsible, cautious risk management," said Kenneth Vecchione, CEO of Western Alliance Bank, in a statement. "This has certainly been a challenging few days for our industry and we appreciate our deep relationships with customers across the bank who continue to choose Western Alliance as their trusted banking resource.”

Charles Schwab is trying to reassure investors its customers are sticking with the financial broker, even as fear escalates about the banking sector.

The company said Friday it has received "strong inflows from clients" over the past week, bringing $16.5 billion in new business. That demonstrates "the trust clients place in Schwab," the brokerage said.

"Charles Schwab remains a safe port in a storm, driven by its conservative balance sheet, strong liquidity position, and diversified base of over 34 million account holders who invest with Charles Schwab every day," the company said in its statement. "We are confident in our approach and in our ability to help clients through all kinds of economic environments."

On Monday, however, Charles Schwab told a very different story. It had said customers had pulled 4% of their assets out of the bank and the amount of money clients owed the bank had fallen 28%.

Schwab's stock was down 3% Friday afternoon, though that was well off the low of the day. Shares have fallen 27% since SVB's bank run a week ago.

The Nasdaq exchange notified SVB on Friday that it will delist SVB Financial Group's stock, according to an SEC filing.

Shares of SVB were halted on March 10, after the bank’s collapse. The suspension will take place on March 28.

Both the company’s common stock and depositary shares will be delisted from the exchange. SVB said it does not plan to contest Nasdaq’s decision.

Stocks deepened their losses Monday afternoon as investors continued to worry about the tumult in the banking sector.

The Dow fell 387 points, or 1.2%. The S&P 500 and Nasdaq slipped 1.1% and roughly 1%, respectively.

The Federal Reserve lent banks a record $153 billion last week, showing the immense pressure weighing down the banking sector on the heels of several failures.

Shares of First Republic continued to get pummeled, falling over 25% despite a decision by a group of big banks to lend it a $30 billion lifeline.

West Texas Intermediate, the US benchmark for oil, was down about 2%.

Gold futures rose 2.1% as investors sought ways to shelter from the banking turmoil.

Investors also digested new consumer sentiment data from the University of Michigan on Friday that showed that Americans' optimism about the economy declined in March for the first time in four months.

The CNN Fear & Greed Index was at 25. That's up from earlier in the week but still indicates extreme fear in the market.

On Tuesday afternoon, JPMorgan Chase CEO Jamie Dimon was in Washington for a previously scheduled banking industry meeting and reached out to Treasury Secretary Janet Yellen and Federal Reserve Board Chair Jerome Powell.

"Very quickly the conversation turned to First Republic," said a source close to the 48-hour deal to infuse First Republic with $30 billion. "The biggest example of a bank that could go down and shouldn't go down -- a first-class bank."

Along with Martin Gruenberg, chairman of the FDIC, the group brainstormed ways to backstop First Republic, fearing a chain reaction through other small banks under pressure from customer withdrawals. Sometime Tuesday afternoon, the idea had gelled to infuse the bank with deposits from other big US banks. They were looking to infuse “confidence and capital” into First Republic.

Treasury Secretary Yellen first proposed cash deposits from other banks and Dimon, Gruenberg and Powell agreed. The first four contributors quickly lined up with $5 billion each. In a statement announcing the deal, JP Morgan, Citigroup, Bank of America and Wells Fargo cited a "commitment to helping banks serve their customers and communities."

Wednesday was a day of phone calls and in person meeting by Dimon, Yellen and others to get more banks on board. In the end 11 banks vowed $30 billion in cash deposits for First Republic.

"There was no special deal, no special rate," the source said, but rather an effort "to pull together and show confidence" in the banking system.

The source said regulators “wanted it to be private-sector solutions. They didn’t want this to be a government bailout.”

The steep selloff in the banking sector on Friday – just a day after a $30 billion rescue of First Republic – is a clear sign that investors still aren’t satisfied with the federal response.

“The market is saying, ‘This is still not enough. We need more,’” Ed Mills, Washington policy analyst at Raymond James, told CNN on Friday.

First Republic shares are plunging 25% in afternoon trading, while PacWest is down 12% and Zions is down 6%.

Big banks are also in the red after injecting $30 billion into First Republic, with JPMorgan Chase down 3% and Bank of America falling 4%.

Mills questioned whether the federal government will eventually need to provide a guarantee for all bank deposits, above the $250,000 limit from the FDIC. He also pointed out that US officials are insisting they don’t want to bail out stockholders even as they rescue depositors.

“This tale of two cities between customers and investors is causing more stress with equities. Can you have one without the other?” Mills asked. 

President Joe Biden is urging Congress to take action to expand the FDIC’s authorities to hold senior bank executives accountable in the wake of the recent Silicon Valley Bank collapse and subsequent fallout in the banking sector.

“No one is above the law – and strengthening accountability is an important deterrent to prevent mismanagement in the future. The law limits the administration’s authority to hold executives responsible,” Biden said in a statement issued Friday. “When banks fail due to mismanagement and excessive risk taking, it should be easier for regulators to claw back compensation from executives, to impose civil penalties, and to ban executives from working in the banking industry again. Congress must act to impose tougher penalties for senior bank executives whose mismanagement contributed to their institutions failing.”

Biden is specifically calling on Congress to take several actions, according to a White House fact sheet also released Friday:

• Expand the FDIC’s authority to claw back compensation – including gains from stock sales – from executives at failed banks like Silicon Valley Bank and Signature Bank
• Strengthen the FDIC’s authority to bar executives from holding jobs in the banking industry when their banks enter receivership
• Expand the FDIC’s authority to bring fines against executives of failed banks

The call on Congress to act comes after Biden on Monday laid out how his administration is taking action to contain Silicon Valley Bank’s collapse. The administration said the federal government was acting to backstop depositors’ funds, make sure taxpayers are not on the hook for these moves, hold those responsible accountable and decline to extend relief to investors of Silicon Valley Bank.