• First Republic rose sharply after falling more than 60% on Monday.
• PacWest and Charles Schwab were also moving higher.
• In addition the backstopping the deposits at SVB and Signature Bank, which was closed on Sunday, federal regulators also announced efforts on Sunday to stabilize the wider banking system.

Shares of First Republic rose sharply on Tuesday as regional banks attempted to rebound from a deep sell-off, but some of the stocks struggled to hold their ground as the day progressed.

First Republic ended the day with a 27.8% gain after climbing more than 60% earlier in the session. PacWest was up nearly 34% after following a similar trajectory, and Charles Schwab added about 9%.

However, the SPDR S&P Regional Banking ETF (KRE) rose just 2% as other regional banks struggled to hold onto their gains. The volatility was evident in Zions Bancorp. and Western Alliance, which each turned negative briefly in afternoon trading after rising earlier in the session. The banks then finished the day with gains of 4% and 14%, respectively.

Those moves come after regional banks fell sharply Monday, even though U.S. regulators took extraordinary measures to backstop all depositors in the now-failed Silicon Valley Bank. The KRE suffered its biggest one-day loss since March 2020, tumbling 12.3%.

First Republic led the way lower on Monday, falling 61.8%. Executive Chairman Jim Herbert told CNBC's Jim Cramer that the bank was not seeing big outflows and was operating as usual. The bank also announced Sunday it received additional liquidity from JPMorgan and the Federal Reserve.

After Tuesday's move, First Republic's stock is still down more than 50% for the week.

While the declines for regional bank stocks Monday showed that many investors were not convinced the regulators' moves would be enough to stop more bank runs, there does not appear to have been widespread withdrawals from banks in recent days, according to Raymond James analyst Daniel Tamayo.

"Outflows did not accelerate during the last few days and, in fact, some banks have seen net inflows given movement in deposits from SVB and Signature Bank," Tamayo said in a note to clients.

Confident statements from finance executives seemed to help support Tuesday's rally. Charles Schwab CEO CEO Walt Bettinger said on CNBC's "The Exchange" that the firm was seeing inflows in "significant numbers." Meanwhile, KeyCorp CEO Chris Gorman said on CNBC's "Squawk on the Street" on Tuesday that his bank has not seen significant deposit outflows in recent days and is actually getting cash inflows from retail customers.

However, First Republic's shares came off their highs of the day after S&P Global put the bank's credit rating under review with negative implications, citing volatile deposit flows. Moody's Investors Service also downgraded its view on the U.S. banking system to negative from stable.

In addition to backstopping the deposits at SVB and Signature Bank, which was closed Sunday, federal regulators also announced efforts Sunday to stabilize the wider banking system. One of those is the Fed's Bank Term Funding Program, which will allow banks to exchange certain high-quality assets for cash without booking mark-to-market losses.

Correction: The Fed on Sunday announced the Bank Term Funding Program. An earlier version misstated the name of the program.