The Labor Department says the four-week average, a less volatile measure, decreased 7,250 to 345,250. Both figures are only about 7,000 above their levels of a month ago, which were the lowest in five years.
Applications are a proxy for layoffs. A decline suggests that companies are cutting fewer jobs. Since January, applications have fallen 6.5 per cent.
At the same time, hiring has been steady. Employers added 175,000 jobs in May, the department said last week. That nearly matched the monthly average for the previous year. The unemployment rate ticked up to 7.6 per cent.