The four-week rolling average rose by 5,500 from the previous week's revised average of 369,250 to 374,750.
The previous week's first-time claims figure was also revised to 388,000 from 380,000.
The biggest increases in initial jobless claims for the week ended April 7 were in Pennsylvania (up 7,483), California (up 6,587) and Washington (up 5,985).
The biggest decreases were recorded in Tennessee (down by 670), Vermont (down 78) and North Dakota (down 49).
The U.S. unemployment rate is 8.2 percent, unchanged from February to March.