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. 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.

The plan is part of an agreement the bank reached in 2008 with state attorneys general involving high-risk loans made by Countrywide Financial Corp. before Bank of America acquired it.

Still, it’s the first time a lender has announced a broad plan to reduce mortgage principal when home values drop well below the amount owed. Bank of America collects more Americans’ home loan payments than any other company.

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.

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.

Bank of America’s effort to reduce foreclosures will affect only some borrowers with especially risky loans. Though other banks could follow its lead, helping 45,000 troubled homeowners won’t make much of a dent in the nation’s foreclosure problem. And forgiving principal could encourage people to default intentionally on their mortgages.

“I don’t necessarily think other banks are going to look at widespread principal forgiveness as a solution,” said Frank Pallotta, managing partner of Loan Value Group, a New Jersey company that’s working with mortgage investors to help cope with the “walkaway” problem.

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.

“The program risks helping few, and for the rest, merely spreading out the foreclosure crisis over the course of several years,” Neil Barofsky, the special inspector general for the federal bailout program, said in a report issued Tuesday.

The more people lose their homes to foreclosure, the more prices will be forced down. Still, some analysts say they don’t expect a drastic plunge in prices in coming years.

“We could see a renewed slide in home prices, but not to the point that it changes things in a big way,” said Wells Fargo economist Mark Vitner.

Home sales were sluggish during the winter even though lawmakers extended a tax credit for first-time homebuyers by five months, to April 30, and expanded it to cover existing homeowners who move. Yet economists, builders and real estate agents say the extension has had little impact on sales.

In its report on new homes, the Commerce Department said sales plummeted in parts of the country that were hit by bad weather. In the Northeast, they fell 20 percent from a month earlier. Midwestern sales fell 18 percent. Sales fell nearly 5 percent in the South but rose 21 percent in the West.

The sales report, which reflects signed contracts rather than completed sales, lets economists assess how many people shopped for new homes in a given month.

The number of new homes up for sale in February rose slightly. At the current sales pace, it would take more than nine months to exhaust that supply.

There was some positive news for builders, though: The median sales price for a new home climbed to $220,500, up more than 5 percent from a year earlier and about 6 percent from January.

Some large homebuilders say their outlook is brightening. Lennar Corp., one of the nation’s largest, reported an 18 percent surge in new home orders and fewer buyers canceling contracts in the last quarter.

Still, said Stuart Hoffman, chief economist at PNC Financial Services Group, falling home sales have signaled a weak start to the year.

“The question is: Is that a prelude to a weak housing market all year long?” AP