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 to 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.

Investors seemed to look past fears that Greece will be forced to default on its bonds — an event that could trigger another financial crisis — and a poor readout of manufacturing conditions in the Northeast from the Federal Reserve Bank of Philadelphia.

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.