Applications remain stuck above the 375,000 level that economists say reflects a healthy job market and would indicate the unemployment rate will fall.
The economy was adding jobs at a fast clip during the last few months of 2011 and into the spring before labor market activity slowed to a crawl.
Employers added 69,000 workers to their payrolls in May, the lowest level this year, raising concerns that the economic recovery was weakening.
But economists have said they expect hiring to pick up again this summer after a lull through the spring that they consider "payback" for the rapid growth over the warm winter, which shifted some hiring.
The June report will be released July 6 and will show whether these estimates are bearing out.