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NEW YORK (CNNMoney.com) -- The number of Americans filing for initial unemployment insurance fell more than expected last week, but ongoing claims ticked higher, according to government data released Thursday.

There were 601,000 initial jobless claims filed in the week ended June 6, down 24,000 from 625,000 the previous week, the Labor Department said.

Economists expected 615,000 new claims, according to a consensus survey by Briefing.com.

"It was a solid improvement," said Adam York, analyst at Wachovia. "These are good signs that we may have seen the peak."

The 4-week moving average of initial claims was 621,750, down 10,500 from the previous week's revised-up average of 632,250.

"That means the job market is starting to get at least 'less worse,'" York said. "The pace of decline is improving, and we aren't seeing huge layoffs like those in January and February."

Continuing claims: The government said 6,816,000 people filed continuing claims in the week ended May 30, the most recent data available. That's an increase of 59,000 from the preceding week's revised-up 6,757,000 claims.

The 4-week moving average of continuing claims rose to 6,750,500, up 57,250 from the prior week's revised average of 6,693,250.

State-by-state data: Thirteen states reported claims decreased by more than 1,000. Florida reported 6,655 fewer claims, which a state-supplied comment attributed to fewer layoffs in the the construction, trade, service, manufacturing and agriculture industries.

No state reported initial claims increased by more than 1,000. That's "certainly a good sign," said York, who expects initial claims will continue declining or flattening.

Outlook: York said he is still worried that ongoing claims will rise.

"The pace of layoffs is slowing, but hiring isn't ready to pick up," he said. "The people who have been laid off aren't picking up new jobs."

A government report released Friday showed that 2.9 million jobs have been lost so far in 2009 and the unemployment rate now stands at 9.4%, its highest level in 26 years.