The Federal Housing Finance Agency (FHFA) said today it will alter a government refinancing program in an effort that could help up to 1 million homeowners who are underwater on their mortgages, Reuters said.

The agency said it was easing the terms of the 2-year-old Home Affordable Refinance Program (HARP), which helps borrowers who have been making mortgage payments on time but have not been able to refinance as home values have dropped.

To help borrowers whose loan balances exceed the value of their homes, FHFA said it will scrap a cap that prohibits any homeowners whose mortgage exceeds 125 percent of the property’s value from participating in HARP, which is targeted at loans backed by Fannie Mae and Freddie Mac.

The plan is the latest government effort to deal with a problem at the center of the economy’s weak recovery — a crippled housing market.

To encourage banks to participate in the program, FHFA is revamping it to protect lenders from having to buy back HARP loans if underwriting problems are later found. Banks will only have to verify that borrowers have made their last six mortgage payments, and the new rules eliminate the need for appraisals in most cases.

The housing agency said it will extend the effort until Dec. 31, 2013. The program is limited to loans that Fannie Mae and Freddie Mac guaranteed before June 2009.