Applications have popped above the 375,000 level economists say reflects a healthy job market and likely means the unemployment rate will fall.
The economy produced a dismal 69,000 jobs in May, the lowest in a year, as the jobless rate increased to 8.2 percent from 8.1, the Labor Department reported last week.
Still, analysts say they expect hiring to pick up this summer to an average of 150,000 to 200,000 jobs a month.
Job growth eclipsed, on average, more than 250,000 a month during the winter before stalling out through the spring. Economists argue that the labor market produced jobs at a faster rate than economic growth and, thus, the past three months have essentially seen a payback for the warm winter hiring.
Federal Reserve Chairman Ben Bernanke will answer questions from lawmakers Thursday morning on whether the central bank will consider additional monetary stimulus down the road if the rate of job creation does not improve this summer.
On Wednesday, the Fed released its "beige book" and reported that the economy and hiring grew at a modest rate this spring.
Those still collecting state-level benefits rose to 3.29 million, up 34,000. Those who are getting federal benefits, usually workers unemployed at least six months, dropped by 105,000 to 2.83 million for the week ended May 19.
Certain levels of federal benefits are gradually being phased out as part of legislation passed earlier this year.
The total number of people claiming benefits in all programs was 5.97 million, a decrease of 167,133 for the week ended May 19.