NEW YORK — Bank of America Corp., faced with a glut of foreclosed and abandoned houses it can’t sell, has a new tool to get rid of the most decrepit ones: a bulldozer.

The biggest U.S. mortgage servicer will donate 100 foreclosed houses in the Cleveland area and in some cases contribute to their demolition in partnership with a local agency that manages blighted property. The bank has similar plans in Detroit and Chicago, with more cities to come, and Wells Fargo, Citigroup, JPMorgan Chase and Fannie Mae are either conducting or considering their own programs.

Disposing of repossessed homes is one of the biggest headaches for lenders in the United States, where 1,679,125 houses, or one in every 77, were in some stage of foreclosure as of June, according to research firm RealtyTrac Inc. of Irvine, Calif. The prospect of those properties flooding the market has depressed prices and driven off buyers concerned that housing values will keep dropping.

“There is way too much supply,” said Gus Frangos, president of the Cleveland-based Cuyahoga County Land Reutilization Corp., which works with lenders, government officials and homeowners to salvage vacant homes. “The best thing we can do to stabilize the market is to get the garbage off.”

Bank of America had 40,000 foreclosures in the first quarter, saddling the Charlotte, N.C.-based lender with taxes and maintenance costs. The bank announced the Cleveland program last month, has committed as many as 100 properties in Detroit and 150 in Chicago, and may add 10 cities by the end of the year, said Rick Simon, a company spokesman.

The lender will pay as much as $7,500 for demolition or $3,500 in areas eligible to receive funds through the federal Neighborhood Stabilization Program. Uses for the land include development, open space and urban farming, according to the statement. Simon declined to say how many foreclosed properties Bank of America holds.

Ohio ranked among the top 10 states with the most foreclosure filings in June, according to RealtyTrac. The state has 71,617 foreclosed homes, Cuyahoga County 9,797 and Cleveland 6,778, RealtyTrac said.

The tear-downs are in varying states of disrepair, from uninhabitable to badly damaged. Simon said some are worth less than $10,000, and it would cost too much to make them livable.