Four years after a massive federal bailout, banks are recording near-record profits — a development welcomed by regulators but met with fresh demands by critics that the financial firms do more to benefit mainstream America.

The industry’s third-quarter earnings jumped 6.6 percent from the same period in 2011, to $37.6 billion, the Federal Deposit Insurance Corp. reported Tuesday. It was the 13th straight quarter of year-over-year increases and the biggest profit since $38 billion in the third quarter of 2006, before the housing bubble burst.

Bert Ely, a bank consultant in Alexandria, Va., said the results reflect a combination of bankers shedding troubled assets, as they have done after previous financial downturns, in a “hardly robust” but nonetheless improving economy.

“We’re seeing a pretty typical recovery, but slower,” Ely said.

RBC Capital Markets analyst Gerard Cassidy said the profits were remarkably high — at a level that, if maintained for a year, would exceed the record for annual earnings, set in 2006.

Analysts had worried over recent reports that showed bank profits had grown largely because banks were merely cleaning up bad loans, and as a result needed fewer reserves against losses. Now the industry’s top line is growing as well, with the home-refinancing boom producing large gains on the sale of mortgages to government-supported financial giants Fannie Mae and Freddie Mac.

“In previous quarters most of the improvement in earnings could be traced to lower provisions for loan losses,” FDIC Chairman Martin J. Gruenberg said. In the latest quarter, he said, “higher revenue contributed more to the increase in earnings than reduced provisions.”

Consumer and labor advocates insisted, though, that it was time for the banks, having benefited from the government bailout, to do more.

“We’re still seeing lenders focused mainly on de-risking,” said Brandon Rees, acting director of the AFL-CIO’s office of investment, which advises union pension plans. “The fact is, banks are not playing their historic role of delivering capital to small businesses and consumers.”

Tom Feltner, director of financial services at the Consumer Federation of America, said, “As many banks turn the corner, I think it’s important for them to … make sure they’re inclusive and not abusive.”

Banks should quit offering short-term, high-interest loans similar to those of payday lenders, he said, and reduce the minimum deposit requirements for fee-free checking.