Mortgage modifications at two of the nation’s largest banks rose in February under a government-backed program, according to federal data.

Bank of America Corp. completed 20,666 mortgage modifications in February under the federal government’s Home Affordable Modification Program, or HAMP, up 61 percent from January, the bank said.

San Francisco-based Wells Fargo & Co. reported a 41 percent increase in permanent modifications over the same period, to 24,975.

The government program provides incentives for banks to modify mortgages if customers are unable to meet the original payment terms. The program is a key component of government efforts to reduce foreclosures.

Homeowners are required to go through a trial modification period before a HAMP modification is made permanent.

Bank of America, the nation’s largest bank by assets, said 22,303 mortgages are in the final stages of being permanently modified, while Wells Fargo, the nation’s fourth largest bank, reported 7,533 are nearly complete.

Wells Fargo said roughly three loan modifications — either through government or company programs — were done for each foreclosure sale of customer homes, from October through February.

Bank of America has 240,000 mortgages in the first stage of the HAMP program, which includes a temporary modification. Wells Fargo reported 139,065 temporary and permanent modifications through the government program.

Overall, Bank of America said it has modified 760,000 mortgages through government and private programs since January 2008. Wells Fargo said it had 505,832 modifications through government-backed and internal programs.