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The four-week moving average for new claims, which irons out week-to-week volatility, rose 4,500 to 352,500.
Although claims have been volatile in recent weeks, there is little in the numbers to suggest a shift in the moderate pace of job gains, even as the broader economy is struggling under the weight of higher taxes and deep government spending cuts.
Last week's data has no bearing on Friday's employment report for May as it falls outside the survey period.
Employers are forecast to have added 170,000 jobs to their payrolls last month, slightly up from April's 165,000 count, according to a Reuters survey. The unemployment rate is seen holding at an almost 4-1/2 year low of 7.5 percent.
(Read More: Companies Spending Cash on Investors, Not Workers)
The labor market is being closely watched for clues to when the Federal Reserve might start scaling back its expansive monetary stimulus.
Fed Chairman Ben Bernanke said last month a decision to start tapering the $85 billion in bonds the U.S. central bank is buying each month could come at one of its "next few meetings" if the economy appeared set to maintain momentum.
The claims report showed the number of people still receiving benefits under regular state programs after an initial week of aid fell 52,000 to 2.95 million in the week ended May 25. The four-week average for the so-called continuing claims was the lowest since May 2008.
(Get the full report here.)