The number of banks on the government’s list of financial institutions most at risk for failure fell for the second consecutive quarter, according to data released Tuesday by the Federal Deposit Insurance Corporation, signaling that the troubles for most American banks may be easing even as Europe’s problems grow worse.

Twenty-one lenders came off the list of so-called problem banks during the third quarter, compared with 23 in the previous period. That brings the total number of troubled banks to 844, or roughly one out of nine lenders.

Not all of those lenders will ultimately fail, but the agency considers them most at risk, making the quarterly update one of the most crucial measures of the industry’s health.

Other signs were mixed. Although the nation’s 7,436 banks registered a nearly 50 percent jump in profit during the third quarter, to $35.3 billion, revenue growth was extremely weak. The bulk of the gains — more than 80 percent, in fact — came from the banks setting less money aside to cover loan losses.

Lending also showed modest improvement, with overall loan balances growing for the second consecutive quarter. The biggest improvement came from loans made to large and midsize corporations, while smaller business loans declined during the period. Home lending remains under stress.

Banks, meanwhile, continued to be flooded with deposits as corporations and consumers flocked to the sidelines amid the gloomy economic reports and the looming fears that Europe’s debt troubles could ripple across the Atlantic. Total deposits rose by more than $234.5 billion, with the nation’s biggest banks receiving about three-quarters of the influx of cash.

Martin J. Gruenberg, the F.D.I.C.’s acting chairman, said that even as the nation’s banks had vastly improved their finances, he remained concerned about the challenges ahead.

“Ongoing distress in real estate markets and slow growth in jobs and incomes continue to pose risks to credit quality,” he said in a statement. “The U.S. economic outlook is also clouded by uncertainties in the global economy and by volatility in financial markets.

Twenty-six banks, most small, were closed during the third quarter. That was four more than in the previous period, but the pace of bank failures has fallen sharply from a year ago, as the agency had expected. There were 74 bank failures through the first nine months of 2011, compared with 127 in the period a year earlier.

The F.D.I.C. insurance fund, which protects the nation’s depositors in the event of a bank collapse, continued to improve. After dipping into the red after the 2008 financial crisis, the fund has been replenished with the help of prepaid premiums and changes to the assessment formula. The fund’s balance now stands at $7.8 billion as of the end of September, up from $3.9 billion at the end of June.

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