WASHINGTON – Fewer Americans applied for unemployment benefits last week, and builders broke ground on more homes in May. The latest data offered some hope that the economy may be improving after hitting a slump in late spring.

Unemployment benefit applications fell to a seasonally adjusted 414,000, the Labor Department said. It was the second drop in three weeks and a positive sign that layoffs are slowing.

Still, applications have been above 400,000 for 10 straight weeks, evidence that the job market is weak compared with earlier this year.

Home construction rose last month to a seasonally adjusted annual rate of 560,000 units per year, the Commerce Department said. Economists say the pace of construction is far below the 1.2 million homes per year that must be built to sustain a healthy housing market. Many credit-strapped builders are struggling to compete with low-priced foreclosures.

The modest improvements in two of the economy’s most troubled areas were enough to give Wall Street a lift after a major sell-off the previous day. The Dow Jones industrial average gained 64 points in afternoon trading. Broader indexes also rose.

Stocks increased despite fears that Greece will be forced to default on its bonds — an event that could trigger another financial crisis there — and after the Federal Reserve Bank of Philadelphia issued a poor report on manufacturing in the region.

Unemployment applications had fallen in February to 375,000, a level that signals sustainable job growth. They stayed below 400,000 for seven of nine weeks. But applications surged in April to 478,000 — an eight-month high — and they have declined slowly since then.

Economists said the steady decline in unemployment applications signals that the job market is improving, but at a very slow pace.

“This is not a derailing of the economy,” said Bricklin Dwyer, an economist at BNP Paribas. “This is a period of weak growth, and we’re going to see this for some time.”

The elevated level of applications suggests that companies pulled back on hiring in the face of higher gas and food prices, which have cut into consumer spending. Hiring has slowed sharply since applications rose.

Employers added only 54,000 net new jobs in May, much slower than the average gain of 220,000 per month in the previous three months. The unemployment rate rose to 9.1 percent from 9 percent.

Employers probably added more jobs in June than in May, but less than the 220,000 pace from earlier this year, economists said.

More hiring is important because it’s key to boosting consumers’ incomes, which in turn would fuel more spending. Consumer spending grew at a weak 2.2 percent annual rate in the January-March quarter, down from 4 percent in the previous quarter. That pushed down economic growth to 1.8 percent from 3.1 percent.

Yet some companies are cutting jobs. Johnson & Johnson said this week it will stop making some of its heart devices because of falling sales, a move that will eliminate up to 1,000 positions. And state and local governments are laying off thousands of employees in order to close large budget deficits.

While the job market was improving earlier this year, home building is coming off the two worst years on records dating back five decades. And the May data suggest that won’t change anytime soon.

The number of single-family homes started in May rose a modest 3.7 percent. But the construction pace of single-family homes, which accounts for about 80 percent of all residential construction, is well below the 2010 rate. Construction of those traditional homes is “still very much dead in the water,” said Mark Vitner, senior economist at Wells Fargo.

Housing permits, a gauge of future construction, rose last month to the highest level since December. But apartment and condominium construction accounted for a large portion of that increase. Renting has become a preferred option for many Americans who lost their jobs in the recession and who were forced to leave their rapidly depreciating homes.

Though new homes represent a small fraction of the overall housing market, they have an outsized impact on the economy. Each home built generates, on average, three jobs and $90,000 in taxes, according to the National Association of Home Builders.

And single-family home purchases ultimately contribute more to the broader economy than apartment sales do. That’s because buyers of single-family homes tend to spend more on furnishings, appliances, landscaping and other home improvements.

Factory output, which has been one of the strongest sectors of the economy since the recession ended two years ago, has also slowed this spring. And it may be getting worse in the Northeast.

The Federal Reserve Bank of Philadelphia said its regional index of manufacturing conditions dropped to -7.7 in June, down from 3.9 in May. It was the first negative reading since last September and the lowest reading for the index since July 2009.

The index tracks manufacturing conditions in the region covered by the Philadelphia Fed. That includes eastern Pennsylvania, southern New Jersey and Delaware.