The department revised last week's estimate from 346,000 to 348,000.
The four-week rolling average for the week increased by 2,750 to 361,250.
The largest increases in initial claims for the week ending April 6 were in New York with a gain of 20,120, North Carolina with a gain of 4,403 and Ohio, up by 3,029.
The largest decreases were in California, down by 12,893, Kentucky by 1,318 and Pennsylvania with 1,299 fewer claims.
Notable deaths of 2014 [PHOTOS]