Bank stocks were under pressure on Wednesday as the sharp drop of Credit Suisse rattled a segment of the market that was already reeling from two large bank failures in the past week.

Shares of the Swiss bank fell more than 27% after its biggest backer said it won't provide further financial support. Credit Suisse announced on Tuesday that it had found "material weakness" in its financial reporting process from prior years. Other European banks also slid, including an 8% drop for Deutsche Bank.

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The move appeared to be hitting large U.S. banks as well. Shares of Wells Fargo and Citi fell more than 4% each in premarket trading, while Bank of America dipped 3%. JPMorgan and Goldman shed more than 2%.

Credit Suisse struggles come on the heels of the collapse of Silicon Valley Bank and Signature Bank in the U.S. Those failures caused steep sell-offs in regional bank stocks on Monday. The SPDR S&P Regional Bank ETF (KRE) fell more than 4% in premarket trading on Wednesday. Zions Bancorp and Western Alliance each fell more than 6%.

While Credit Suisse's struggles appear unrelated to the mid-tier U.S. banks, the combination of the two issues could spark a broader reexamination of the banking system among investors, according to Peter Boockvar of Bleakley Financial Group.

"What this is telling us is there's the potential for just a large credit extension contraction that banks are going to embark on [to] focus more on firming up balance sheets and rather than focus on lending," Boockvar said on CNBC's "Squawk Box."

"It's a balance sheet rethink that the markets have. Also you have to wonder with a lot of these banks if they're going to have to start going out and raising equity," he added.

In that vein, Wells Fargo on Tuesday filed to raise $9.5 billion of capital through the sale of debt, warrants and other securities. The bank said the new cash will be used for general corporate purposes.

The fallout from the collapse of SVB could also lead to more regulation and rising costs for the U.S. banking sector, including the potential for higher fees to regulators to pay for deposit insurance.