In the week ending June 6, the advance figure for seasonally adjusted initial claims was 1,542,000, a decrease of 355,000 from the previous week's revised level, according to the Department of Labor. The previous week's level was revised up by 20,000 from 1,877,000 to 1,897,000. The 4-week moving average was 2,002,000, a decrease of 286,250 from the previous week's revised average. The previous week's average was revised up by 4,250 from 2,284,000 to 2,288,250.
The U.S. economy also added 2.5 million jobs in May and the unemployment rate declined to 13.3% from the prior report’s 14.7%, according to the Bureau of Labor Statistics. 
The unemployment rates decline in May for adult men to 11.6%, adult women (13.9%), Whites (12.4%), African Americans (16.8%), and Hispanics (17.6%).
Construction employment rose by 464,000 in May—gaining back almost half of April’s decline (-995,000). Much of this gain was attributed to specialty trade contractors, with the increase split between the residential and nonresidential components.
Realtor.com’s Chief Economist Danielle Hale said the share of works who expect to return to work within six months remains higher than normal, but “that’s one of the few bright spots in an otherwise dismal report.”
“Even workers expecting only a short disruption in income likely cut back on spending and dipped into savings to make ends meet. Unemployment benefits, which are currently more generous than usual, will help, but major purchases such as cars and homes may be delayed for some buyers until they feel like the jobs market is back to normal,” Hale said. “The longer the disruption in the labor market, the longer consumers may have to wait on making major purchases such as cars and homes.”
For the week ending May 23, the states and territories with the highest insured unemployment rates were Maine (26.9%), Nevada (24.3%), Michigan (21.7%), Hawaii (20.1%), and Puerto Rico (19.0%). The national figure for the corresponding week was 14.6%. The insured unemployment rate represents the fraction of the unemployment insurance-eligible workforce currently receiving benefits. For the week ending May 30, Florida and Oregon showed the largest increases in continued claims, rising 306,000 and 201,000, respectively, from the prior week, while Pennsylvania and Texas had the largest declines, falling 166,00 and 160,000, respectively, from the prior week. (All state-level data for the week ending May 30 should be considered preliminary estimates due to the way these data are collected)
"As with the prior weeks, a few caveats make this week’s data difficult to interpret precisely," said Fannie Mae Chief Economist Doug Duncan. "On one hand, unemployment insurance eligibility rules have been relaxed recently, increasing the number of people who are able to apply. This makes it difficult to estimate the uninsured unemployed share of the workforce. On the other hand, many states reported a significant backlog of unemployment insurance applications due to a lack of processing capacity, indicating that this week’s release may understate the true extent of insured layoffs.”