The four-week rolling average for the week ended Saturday was 424,750, a decline of 3,000 from the previous week's revised average, the department said.
In May, the national unemployment rate was unchanged at 9.1 percent, as the economy added 54,000 jobs in the month, a sharp slowdown from the first four months of the year.
However, payroll firm Automatic Data Processing Inc. said 157,000 private sector jobs were added to the economy in June.
The Labor Department's monthly employment situation report is due Friday.
For the week ending June 25, the largest increases in initial claims were in New Jersey and California, where claims rose by 6,827 and 5,375, respectively. The largest declines were in Pennsylvania, where first-time claims dropped by 4,974 and Puerto Rico, where first-time claims dropped by 1,332.