The increase comes after claims fell sharply in the prior two weeks, but difficulties in adjusting for seasonal factors can distort the numbers, the Labor Department said.
The four-week moving average of claims edged up last week to 386,000. However, the moving average has been below the 400,000 mark -- a level associated with weakness in the job market -- for seven straight weeks.
Still, many economists believe that jobs growth for July will be sufficient to keep the nation's unemployment rate steady at 5.9 percent.
Economists are forecasting the addition of around 66,000 jobs in July.