WASHINGTON – The Obama administration’s effort to help those at risk of losing their homes is failing to aid many of them, and that could be followed by a rise in foreclosures that would further depress the housing industry.

More foreclosures would force down home prices, and that would deter already-ailing home builders from starting new projects.

As a result, the economic rebound could suffer. Each new home built creates, on average, the equivalent of three jobs for a year and generates about $90,000 in taxes paid to local and federal authorities, according to the National Association of Home Builders.

“Foreclosures hold down the pricing for everybody,” said Marty Mitchell, vice CEO of Mitchell & Best Home Builders in Rockville, Md. “As a builder, we have to be cognizant of foreclosures, if there are more coming along, because it affects pricing across the board.”

Construction of new homes and apartments fell 5 percent in June from a month earlier to a seasonally adjusted annual rate of 549,000, the lowest level since October, the Commerce Department said Tuesday. May’s figure was revised downward to 578,000.

Driving the decline was a more than 20 percent drop in condominium and apartment construction, a small but volatile portion of the housing market. Construction of single-family homes, the largest part of the market, was essentially flat.

The home construction report was released one day after the National Association of Home Builders said that its monthly reading of builders’ sentiment about the housing market sank to the lowest level since March 2009.

“We’re going to see very minimal new construction until the stream of foreclosures has ended,” said Jack McCabe, a real estate consultant in Deerfield Beach, Fla.

The glut of homes being sold at foreclosure or as short sales — when a bank agrees to accept less than the total mortgage amount — could rise even faster in the months ahead.

More than 40 percent of the 1.3 million homeowners enrolled in the Obama administration’s mortgage relief effort have fallen out of the program, the Treasury Department said Tuesday.

“The program really hasn’t helped a lot of people, or at least not nearly as many had been hoped for,” said Mark Zandi, chief economist at Moody’s Analytics. He predicts that about 2 million homes are likely to be sold over the next 12 to 18 months as foreclosures or short sales.

Many borrowers have complained that banks often lose their documents and then claim borrowers did not send back the necessary paperwork.

The banking industry said borrowers weren’t sending back the necessary paperwork. They also have accused the Obama administration of initially pressuring them to sign up borrowers without insisting first on proof of their income. When banks later moved to collect the information, many troubled homeowners were disqualified or dropped out.

Obama officials dispute that they pressured banks, and they defend the program. Lenders are making more significant cuts to borrowers’ monthly payments than before the program was launched. And eight of the largest mortgage companies in the program have offered alternative programs to 45 percent of those who fell out of the program.

The government’s program “only reflects a portion of what’s happening in the broader marketplace,” said Raphael Bostic, an assistant secretary at the Department of Housing and Urban Development.

While developers have cut back on construction and the number of new homes on the market has fallen dramatically, they still must compete against foreclosed homes.

Builders are adjusting by adopting a new sales pitch. Many are emphasizing the simplicity of buying a new home, compared with the bureaucracy involved with purchasing a short sale or the expense of repairing a foreclosed property.

The rate of home building is still up about 15 percent from the bottom in April 2009, though it’s down 76 percent from the last decade’s peak in January 2006.

New home sales in May dropped 33 percent to the slowest pace in the 47 years that records have been kept. The drop-off came immediately after the tax incentives to sign a contract on a home ended April 30.

Builders may be turning their attention away from new projects to complete those already in progress. Housing completions rose 26.2 percent in June.

But Mitchell said many are focusing on existing projects because they can’t get financing for new ones.

“Banks just don’t want to get involved with any new real estate deals whatsoever,” he said. “Particularly for the private builders, the only choice you have is to build out the projects that you’re in.”Many builders are emphasizing the simplicity of buying a new home, compared with the bureaucracy involved with purchasing a short sale or the expense of repairing a foreclosed property.