First-time jobless claims fell by 2,000 in the week ended Saturday, the U.S. Labor Department said.
Initial claims for unemployment benefits fell to 387,000 from the previous week's revised estimate of 389,000.
The four-week rolling average, which gives a steadier indication of the direction of jobless claims rose by 3,500 to 386,250.
The largest increases in initial claims for the week ending June 9 were in California (up by 12,987), Pennsylvania (up by 7,036) and Texas (up by 4,028). The largest decreases were in Missouri (down by 438), Alaska (down by 126) and Puerto Rico (down by 99).
The U.S. unemployment rate is 8.2 percent, having risen 0.1 of a percentage point from April to May.