The department revised last week's estimate from 323,000 to 328,000, erasing some of the recent gains before the latest weekly figures even came in.
The four-week rolling average for the week rose by 1,250 to 338,000.
The largest increases in initial claims for the week ending May 4 were in Georgia with a jump of 2,212, New Mexico with 1,539 additional first-time claims and Kentucky with a gain of 892.
The largest decreases were in Connecticut with a drop of 1,434, New Hampshire with a drop of 867, and Massachusetts, where first-time claims fell by 756.
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