Shares of banking stocks in the U.S. tumbled on Tuesday after Fitch Ratings warned of the possibility of a downgrade of several lenders, raising investor concerns about the overall health of the banking sector.The U.S. banking sector may be close to another source of turbulence, according to a report by CNBC quoting a Fitch Ratings analyst. This could also lead to "sweeping rating downgrades" across several lenders, including JPMorgan Chase, it said. In June, Fitch also downgraded the score of the U.S. banking sector's 'operating environment' to 'AA-' from 'AA', raising concerns over the health of the sector. However, with industry behemoths like JPMorgan Chase now under surveillance, concerns have only increased, triggering a broad sell-off.Adding to this, the possibility of the Federal Deposit Insurance Corporation proposing changes in the regional U.S. banking living wills further sparked investor concerns.The rules are part of the several changes being introduced by U.S. regulators in order to keep the banking sector under watch after the fall of the Silicon Valley Bank and some others.Wall Street's benchmark S&P 500 fell 1.16% to close at 4,437.86. Major U.S. banks dragged the market, with JP Morgan Chase falling almost 3%, Bank of America down 3.2%, Morgan Stanley falling 1.34%, and Goldman Sachs Group declining 1.6%.U.S. bank stocks were under pressure even last week when Moody's downgraded several banks on grounds of weaker profitability and funding risks. This included slashing ratings by one notch on 10 small-to-mid-sized banks and placing six large banks, including Bank of New York Mellon and U.S. Bank Corp., under review for potential downgrades.Recently, Fitch also downgraded the U.S. Sovereign rating from 'AAA' to 'AA+' after citing expected fiscal deterioration over the next three years, and a high and growing general government debt burden.High-Yield Default Rate To Climb As Pressures Mount, Fitch Says