Applications are a measure of the pace of layoffs. When claims dip below 375,000, it typically suggests hiring is strong enough to reduce the unemployment rate. They have hovered near that level for most of the year after declining sharply last fall.
"Although the labor market appears to have stabilized, and is stronger than it was in 2011, it is not particularly robust," Steven A. Wood, chief economist at Insight Economics wrote in a note to clients.
The government last week reported that employers added just 69,000 jobs in May, the fewest in a year. The unemployment rate rose to 8.2 percent from 8.1 percent in April.
Job growth averaged a decent 252,000 a month from December through February. That helped lower the unemployment rate from 9.1 percent in August.
But hiring has slowed in the past three months to an average 96,000 a month.
The number of people receiving benefits is falling, partly because extended benefit programs are ending in many states. About 6 million people received benefits in the week ended May 19, the latest data available. That's a drop of 167,000 from the previous week.
The economy is still struggling three years after the recession officially ended in June 2009. Wages haven't kept up with inflation, pinching consumer spending. State and local governments have continued to shed jobs.
The government reported last week that the economy grew at a sluggish annual rate of 1.9 percent the first three months of 2012, which is consistent with monthly job growth of around 90,000.