U.S. banks are enjoying their best profits in six years and are lending a bit more freely. The gradual improvement suggests that the industry will sustain its healing from the worst financial crisis in decades and help strengthen the economy.

The industry earned $37.6 billion from July through September — a 6.6 percent increase from its earnings in same quarter last year.

For the first time since 2009, the stronger earnings were due mainly to higher revenue rather than to less money set aside by the banks to cover losses, data issued by the Federal Deposit Insurance Corp. showed Tuesday. And loans to consumers rose nearly 1 percent from the July-September period of 2011.

“We are seeing the classic recovery from a recession,” said Bert Ely, a banking industry consultant based in Alexandria, Va. “All of the arrows are pointing in the right direction.”

Some of the largest banks are cautioning, though, that their earnings are up mostly because they’ve sold less-profitable businesses, shed bad loans and trimmed jobs — not because of a more vibrant economy.

Some banks are testing higher fees on consumer loans and services to offset new rules mandated after the crisis that have crimped revenue.

Consumer lending grew in most categories in the third quarter. That shows banks are becoming less cautious, which could help the economy. More lending leads to more consumer spending, which drives roughly 70 percent of economic activity.

The banks’ mortgage loans increased 0.8 percent from the previous quarter. Auto loans jumped 2.4 percent.