NEW YORK (CNNMoney.com) -- The number of first-time filers for unemployment insurance fell last week, according to a government report released Thursday.
There were 453,000 initial jobless claims filed in the week ended May 29, down 10,000 from an upwardly revised 463,000 the previous week, the Labor Department said.
A consensus estimate of economists surveyed by Briefing.com expected 455,000 new claims for the week. The report was released a day later than usual because of Monday's Memorial Day holiday.
The 4-week moving average of initial claims was 459,000, up 1,750 from the previous week. Moving averages aim to smooth out week-by-week volatility.
"This is a relief, but it is hardly comforting," said Ian Shepherdson, economist at High Frequency Economics, in a research note.
Initial claims have held around the 450,000 mark recently, Shepherdson said, "capturing the still-terrible state of the small-business sector, but (they) do not reflect the much better story among larger firms."
Continuing claims: The government also said 4,666,000 people filed continuing claims in the week ended May 22, the most recent data available. That's up 31,000 from the preceding week.
The 4-week moving average for ongoing claims rose by 9,750 to 4,654,000.
Continuing claims reflect people who file each week after their initial claim until the end of their standard benefits, which usually last 26 weeks. The figures do not include those who have moved to state or federal extensions, nor people who have exhausted their benefits.
A separate report Thursday showed private-sector employers added 55,000 jobs to their payrolls in May, for the fourth straight monthly gain.
Coming up Friday, the widely watched jobs report from the Department of Labor is expected to show employers added 500,000 jobs to their payrolls after adding 290,000 the previous month, according to a consensus of economists surveyed by Briefing.com. The unemployment rate is expected to ease to 9.8% from 9.9% in April.
State-by-state data: Two states said initial claims rose by more than 1,000 for the week ended May 22, the most recent data available.
Claims in New York increased by 1,556, which a state-supplied comment attributed to layoffs in the construction, trade and service industries. Missouri saw claims increase by 1,189.
Six states said new claims fell by more than 1,000. Michigan said claims fell by 2,269, Tennessee had 1,808 fewer claims, Pennsylvania's dropped by 1,597, Georgia's fell by 1,544 and California claims fell 1,206. 
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