WASHINGTON — Under a policy announced Thursday, thousands of borrowers on the verge of foreclosure soon will have the option of renting their homes from Fannie Mae.

The government-controlled company, through its new “Deed for Lease” program, will allow borrowers to transfer ownership to Fannie Mae and sign a one-year lease, with month-to-month extensions after that.

The program will “eliminate some of the uncertainty of foreclosure, keep families and tenants in their homes during a transitional period and help to stabilize neighborhoods and communities,” Jay Ryan, a Fannie Mae vice president, said in a statement.

But the effort is likely to affect a relatively small number of homeowners. In the first half of the year, Fannie Mae took back about 1,200 properties through this process, known as a deed-in-lieu of foreclosure. That pales in comparison with the 57,000 foreclosed properties the company repossessed in the period.

While neither option is particularly attractive for the homeowner, a deed-in-lieu does less harm to the borrower’s credit record.

The rental program is designed to help homeowners who don’t qualify for a loan modification under the Obama administration’s plan, but still want to stay in in their homes. Fannie Mae would not market the homes for sale during the one-year rental period.

Fannie Mae has hired an outside company, which officials declined to identify, to manage the properties.

To qualify, homeowners have to live in the home as their primary residence and prove that they can afford the market rent, which would be determined by the management company. The rent can’t be more than 31 percent of their pretax income.

Freddie Mac, Fannie Mae’s sibling company, launched a similar effort in March. But it requires the foreclosure to be complete and allows only month-to-month leases.

A Freddie Mac spokesman declined to say how many borrowers have participated.