The Labor Department said Thursday that the less volatile four-week average increased by 2,500 to 348,250.
Applications are a proxy for layoffs. Since January, they have fallen 6 percent. That suggests companies are cutting fewer jobs.
At the same time, hiring has been steady, despite an increase in taxes on Jan. 1 and steep federal spending cuts that began in March. Solid consumer spending and a rebound in housing have helped the economy weather the fiscal drag.
Jennifer Lee, an economist at BMO Capital Markets, said the increase in applications makes it less likely that hiring will accelerate this month but job growth remains moderate.
"The overall U.S. labor market is improving," Lee said.
Employers added 175,000 jobs in May, nearly matching the average monthly gain for the past year. The unemployment rate ticked up to 7.6 percent from 7.5 percent, but for a good reason: More Americans were confident they could find work and began searching for a job.
The Federal Reserve on Wednesday offered a brighter outlook for the job market and economy. Chairman Ben Bernanke said the Fed is likely to reduce its bond purchases later this year and end them in the middle of next year if the economy continues to strengthen.
The Fed expects the unemployment rate will fall to between 6.5 percent and 6.8 percent by the end of 2014. That's lower than their March forecast of 6.7 percent to 7 percent.
About 4.5 million Americans received unemployment benefits in the week ending June 1, the latest data available. That's 18,000 more than the previous week. But the number of recipients has fallen 28 percent in the past year. Some have likely gotten jobs, but many have used up all the benefits available.
The Labor Department said last week that more Americans quit their jobs in April compared with March. That points to confidence in the job market, since most workers don't quit until they have another job or are sure they can find one. More quits also opens up jobs for other workers, or the unemployed, to take.
Also last week, a survey of chief executives at the largest U.S. companies showed that they are more optimistic about sales in the next six months and plan to add more workers.
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