The number of banks on the U.S. 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 Corp., signaling that the troubles for most U.S. 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 — 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; smaller business loans actually 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.