First Republic led a comeback rally in regional bank shares Tuesday, as investors hoped for some sort of strategic action by the troubled bank — or another big regulatory move — to stem the downward spiral in the sector.

CNBC's David Faber reported Monday that JPMorgan Chase is giving advice on alternatives to the San Francisco bank that's drawn the attention of Wall Street for its large amount of uninsured deposits, similar to failed Silicon Valley Bank. Those alternatives include a capital raise or possibly even a sale, sources told Faber.

First Republic shares soared 22% in Tuesday premarket trading, following a 90% plunge so far in March. The SPDR S&P Regional Banking ETF gained 3.3% in early trading, following a 29% slide in March so far.

Also helping sentiment was a report by Bloomberg News that the Treasury Department is studying whether regulators have the authority to temporarily insure deposits above the current Federal Deposit Insurance Co. cap without approval of Congress, citing people with knowledge of the talks. Though, the report said these government officials don't believe such drastic action is necessary yet.

"There has been speculation that the limit could be doubled, and further speculation that the FDIC could decide to insure all deposits," wrote Alexander Twerdahl, a Piper Sandler analyst, in a recent note. "In actuality, it would take an act of Congress to change the FDIC's insurance limit and our understanding is that it isn't an issue that is likely to be taken up any time soon."

JPMorgan led a group of 11 banks last week that deposited a combined $30 billion into First Republic, but its stock has continued to decline. Part of the rescue plan for First Republic could entail converting some of that deposit money into a capital infusion, the Wall Street Journal reported, citing sources.

KeyCorp, Citizens Financial, U.S. Bancorp and Huntington Bancshares were all up more than 3% Tuesday in early trading.

First Republic shares hit a record low Monday.

— CNBC's Michael Bloom contributed reporting.