The Federal Housing Finance Agency announced Monday that it will begin taking bids from investors to buy clusters of foreclosed properties and turn them into rentals.

The agency, which oversees government-backed mortgage giants Fannie Mae and Freddie Mac, said the pilot bulk sale program would focus initially on some of the country’s hardest-hit cities — Atlanta, Chicago, Las Vegas, Los Angeles and Phoenix, as well as parts of Florida.

Last summer, the FHFA, along with the Treasury Department and the Department of Housing and Urban Development, solicited outside input for creative ways to help answer a perplexing question: How could the government rid itself of the glut of foreclosed properties it now owns in a way that nudges the housing market toward recovery?

Fannie and Freddie have taken possession of hundreds of thousands of foreclosures throughout the country since the housing bust. But selling those homes at decent prices in an abysmal market has proven tough.

The new initiative is intended to help the government clear the backlog on its books, meet increasing rental demands and help relieve pressure on local housing prices.

To qualify for participation in the program, potential investors must post a security deposit, sign a confidentiality agreement and submit a detailed application showing they have the experience and means to purchase and manage the properties. That application will be reviewed by an outside firm, FHFA said.