WASHINGTON — The Obama administration is making it easier for out-of-work homeowners to stay in their homes, as it tries to revamp its signature but troubled foreclosure-prevention program.

Starting Aug. 1, the Federal Housing Administration will extend the period for unemployed homeowners to miss mortgage payments from three or four months to a full year. That will allow qualified homeowners to go without making a monthly payment for 12 months before the foreclosure process begins.

The extended grace period only applies to FHA-backed loans, which represent about 14 percent of all active mortgages and roughly 25 percent of new mortgages, and homeowners in the government’s foreclosure-prevention program.

Housing and Urban Development Secretary Shaun Donovan said today that administration officials hope private lenders and government-controlled mortgage giants Fannie Mae and Freddie Mac, which back 90 percent of all new mortgages, will adopt a similar policy.

“Our hope is that this will have broader effects,” Donovan said during a conference call.

The government launched its chief foreclosure program in 2009 to help those at risk of foreclosure by lowering their monthly payments. Borrowers start with lower payments on a trial basis. But the program has struggled to convert them into permanent loan modifications.

More than 1.6 million troubled homeowners received trial modifications over the past two years. But a majority of the applicants, about 854,000 homeowners, have dropped out of the program entirely.

In recent weeks, administration officials have acknowledged that housing has become a significant drag on the economy. President Barack Obama said the housing market has “been most stubborn to us trying to solve the problem,” during a town-hall-style meeting Wednesday on Twitter.

Homeowners accepted into the program receive interest rates as low as 2 percent for five years. They can repay their loans over a longer period. The median savings for those who remain in the program is about $526 per month.

Those who have their payments delayed must repay them, with interest.

But many homeowners have complained that the program has been a bureaucratic mess. Some have said they were disqualified after banks lost their documents and failed to return their phone calls. Banks have blamed homeowners for failing to submit needed paperwork.