The Federal Housing Finance Agency introduced new rules Monday that will give more “underwater” homeowners, those who owe more on their homes than they’re worth, the chance to refinance their mortgages at lower rates through the federal Home Affordable Refinance Program.

Officials said historically low interest rates make it a good time for homeowners to reduce monthly payments through the program, which could help many avoid foreclosure or create more cash for household spending.

The agency estimates that almost a million homeowners could take advantage of the program by the end of 2013. The program began in early 2009 but has helped far fewer borrowers than expected - nearly 894,000 through Aug. 31.

Previously, only those who owed more than 25 percent above their home’s value were eligible for the program. Now there is no limit.

Certain fees for those who refinance also have been reduced or eliminated, and a new property appraisal won’t be required if Fannie Mae or Freddie Mac have an estimate for the residence.

Only loans backed by Fannie Mae and Freddie Mac are eligible for the program.

The companies will issue details by Nov. 15 to mortgage lenders and servicers, which set their own schedules and are not required to participate.