WASHINGTON — The recovery in the housing market is at risk of collapsing.

Home sales are sliding, prices are stalling and foreclosures are rising. And mortgage rates are likely to go up after next week, when the Federal Reserve ends a program that has driven them down.

The trend could threaten the broader economy, economists warn. People whose home equity is stagnant or shrinking are less likely to spend freely.

Only a few months ago, the housing market had been showing signs of strength as it recovered from the most painful downturn in decades. Much of the improvement, though, came from government programs that held down mortgage rates and provided tax breaks for buyers. Since the fall, sales have sunk. And the government support is running out.

The latest sour news came Wednesday, when the Commerce Department said sales of new homes fell last month to their lowest point on record. It was the fourth straight drop.

“While bad weather could well have suppressed the February result, it was dismal no matter how one tries to slice and dice it,” wrote Joshua Shapiro, chief U.S. economist at MFR Inc.

That news followed a report a day earlier that sales of existing homes fell for the third straight month in February, to their lowest level since July.

In a move that will help at least some homeowners avoid foreclosure, Bank of America unveiled a $3 billion plan Wednesday to help some of its most troubled borrowers. It said it will forgive up to 30 percent of their total mortgage balance. About 45,000 borrowers are expected to qualify, the bank said.

To cope with falling demand, the homebuilding industry has slashed the pace of construction. But thousands of foreclosed homes have been dumped on the market at bargain prices. That glut has made it hard for builders to compete.

Prices have followed sales down. The median sales price for previously occupied homes fell to $165,100 in February, down from a peak of $230,300 in July 2006, according to the National Association of Realtors.

Falling home prices mean builders can’t recoup their construction costs. And that means fewer construction jobs.

It also signals that the building industry won’t be giving much of a lift to the economic recovery. Each new home built creates about 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.

Experts have been forecasting for months that home prices will fall again after rising steadily since last spring. That’s because hundreds of thousands of foreclosed homes have yet to hit the market at deeply discounted prices.

The Obama administration’s program to prevent foreclosures has so far been a dud. Only 170,000 homeowners had completed the loan modification process as of last month, out of 1.1 million who started it over the past year. Critics have urged the government to do more.