The high level of jobless claims is a sign that many laid-off workers are having difficulty finding new work.
New jobless claims rose more than expected last week, while the number of workers continuing to filing claims for unemployment benefits topped 6.1 million.
Both figures are fresh evidence layoffs persist amid a weak job market that is not expected to rebound anytime soon.
The Labor Department said Thursday initial claims for unemployment compensation rose to a seasonally adjusted 640,000, up from a revised 613,000 the previous week. That was slightly above analysts' expectations of 635,000.
Economists are closely watching the unemployment compensation data because they believe a sustained decline in the number of initial claims could signal the end of the recession is nearing. Jobless claims have historically peaked six to 10 weeks before recessions end, according to a report by Goldman Sachs. Initial claims reflect the level of job cuts by employers.
But the latest report shows job losses remain high. The four-week average of claims, which smooths out volatility, dropped slightly to 646,750, about 12,000 below the peak in early April. Goldman Sachs economists have said a decline of 30,000 to 40,000 in the four-week average is needed to signal a peak.
In another sign of labor market weakness, the number of people continuing to claim benefits rose to 6.13 million, setting a record for the 12th straight week. As a proportion of the work force, the total jobless benefit rolls are the highest since January 1983. The continuing claims data lag initial claims by a week.
The high level of continuing claims is a sign that many laid-off workers are having difficulty finding new jobs.
Employers have cut 5.1 million jobs since the recession began in December 2007 in an effort to slash costs as consumers and businesses have sharply reduced spending. The department said earlier this month that companies cut a net total of 663,000 jobs in March, sending the unemployment rate to 8.5 percent, the highest in 25 years.
The Obama administration is counting on its $787 billion stimulus package, enacted in February, to "save or create" 3.5 million jobs.