The four-week rolling average decreased by 4,250 from the previous week's revised average of 366,000.
The previous week's figure on first-time benefit claims was also revised to 363,000 from 359.000.
Still, employment news has been positive of late. First-time claims have dropped in four of the past five weeks and Automatic Data Processing Inc. said this week that 209,000 private sector jobs were added to the economy in March.
The biggest increases in initial jobless claims for the week ended March 24 were in Texas (up 4,185), California (up 2,199),Kansas (up 1,555), Arkansas (up 1,141) and Washington (up 714).
The biggest decreases were recorded in Pennsylvania (down 1,956), North Carolina (down 1,656), New Jersey (down 1,511), Massachusetts (down 1,083) and Hawaii (down 650).
Florida bear attack: Black bear mauls woman's face
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'