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WASHINGTON — The number of people filing for unemployment last week rose slightly more than expected to 558,000, another reminder that despite other indications of improvement in the economy, the job market remains weak.

First-time claims increased 4,000 compared with the previous week, while the four-week moving average, which smooths out week-to-week volatility, rose by 8,500 to 565,000, the Labor Department reported Thursday. That is still below what it was 18 weeks ago and suggests that initial jobless claims have peaked.

Federal Reserve leaders on Wednesday gave an upbeat assessment of the economy, saying economic activity was “leveling out.” And they left a key interest rate they control close to zero.

Analysts noted, however, that initial claims will likely have to fall below 400,000 before the economy stops shedding jobs. More than 14 million Americans are out of work, and data issued this week by the Labor Department showed there are six unemployed people for every job opening.

The jobs report for July, which came out last week, showed that businesses cut fewer jobs in July and that the nation’s unemployment rate dipped to 9.4 percent. But most economists are predicting unemployment will rise to 10 percent by year’s end.

A separate report released by the Commerce Department on Thursday showed businesses slashed inventories at a faster-than-expected pace of 1.1 percent in June, in part because of an increase in auto sales. Auto sales are expected to keep rising as a result of the “cash for clunkers” program.

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