The bank's stock is also the worst performer among U.S. regional lenders after shedding 90% of its market value in March following the implosion of Silicon Valley Bank.

First Republic was last trading at $16.67, a day after missing out on a broader rally in bank stocks even as large U.S. lenders infused $30 billion to allay fears over the San Francisco-based bank's funding.

Despite Tuesday's rebound, some investors were skeptical of First Republic's stability.

"We do not believe First Republic can survive on its own without a recapitalization deal," said Jason Benowitz, senior portfolio manager at CI Roosevelt.

The volatility in its shares reflects shifting probabilities, including a bank failure that might leave the stock worthless, a recapitalization that would likely be highly dilutive relative to book value, or a sale that might be also highly dilutive, Benowitz said.

First Republic's bonds due 2047 edged up 4 cents on the dollar to trade at 59 cents after closing at a record low on Monday.

Those notes were trading at 83 cents on the dollar a day before Silicon Valley Bank was shuttered on March 10.

First Republic's market cap has shrunk to $2.2 billion from about $22.5 billion in 14 sessions this month.

Fears of contagion in the regional banking sector triggered a market rout last week that has not been seen since Russia invaded Ukraine, a Bank of America's Global Fund Manager Survey showed.

Other regional lenders also ticked higher, with PacWest Bancorp and Western Alliance Bancorp adding about 11% each.

U.S. banking system is stabilizing, but further steps to protect bank depositors may be warranted if smaller institutions suffer deposit runs, U.S. Treasury Secretary Janet Yellen said.

For now, it is clear that the U.S. government will step in and protect depositors, 50 Park Investments CEO Adam Sarhan said.

"If that happens, these stocks will not go to zero ... (which) means they are very cheap right now so value investors are attracted and buying at these low levels," Sarhan added.