Claims for unemployment benefits fell more than expected last week, pointing to further modest improvement in the job market.

About 334,0000 people filed for their first week of jobless benefits last week, 12,000 fewer than a week earlier, the Department of Labor said. It was the lowest level since early May, and slightly better than the 345,000 claims economists had expected.

Initial claims are a choppy indicator from week to week but have largely been hovering around levels last seen in early 2008. That data coincides with other reports showing that layoffs are back to pre-recession levels.

Hiring for new jobs, however, remains sluggish. The government's latest jobs report showed employers added 175,000 jobs in May, falling in line with average job growth over the last three years.

Nearly 12 million people remain unemployed, but only a fraction of them are collecting benefits.

The latest initial claims report shows 2.97 million people filed for their second week or more of unemployment benefits in the week ending June 1, the most recent data available. That was up by 2,000 from the prior week.