Applications are up slightly from a five-year low hit about a month ago.
The Bureau of Labor Statistics will release May's job figures on Friday, which could run between 160,000 and 170,000.
In a separate report on Thursday, monthly job cuts declined for the third consecutive month in May. Employers announced plans to trim payrolls by 36,398, 4.5 percent fewer than in April.
The May total was 41 percent lower than the same month a year ago, when employers slashed payrolls by 61,887, according to the report from global outplacement consultancy Challenger, Gray & Christmas.
So far this year, employers have announced 219,560 planned job cuts, down 11 percent from the 245,540 planned cuts announced in the first five months of 2012.