The four-week rolling average rose by 4,250 from the previous week's revised average of 364,250 to 368,500.
The previous week's first-time claims figure was also revised to 367,000 from 357,000.
The biggest increases in initial jobless claims for the week ended March 31 were in Oregon (up 2,079), Pennsylvania (up 1,866), Illinois (up 1,024) and New Jersey (up 725).
The biggest decreases were recorded in Texas (down by 1,633), Florida (down 1,556), New York (down 1,216), and Puerto Rico (down 928).
The U.S. unemployment rate is 8.2 percent, unchanged from February to March.