* U.S. new jobless claims fall again last week
* Continuing claims drop for the first time since Jan. 3
* Productivity accelerates in Q1, hours worked plunge
By Lucia Mutikani
WASHINGTON, June 4 (Reuters) - Fewer U.S. workers filed new claims for jobless benefits for a third straight week last week and productivity rose at a stronger-than-expected pace in the first quarter, data showed on Thursday, supporting budding hope that the recession was losing force.
Initial claims for state unemployment insurance benefits fell 4,000 to 621,000 in the week ended May 30, the Labor Department said. The week covered the Memorial Day holiday, which could have had an impact on the data.
There was even more goods news in the report as the number of people staying on the benefit rolls after collecting an initial week of aid fell for the first time since January.
In another report, the department said non-farm productivity was much stronger than initially estimated in the first quarter.
"It's good news with respect to the fact that we're looking like we turned the corner in terms of the claims. That's a sign that we're close to the end of the recession, if it holds, and we're also seeing that kind of data in other indicators," said Michael Darda, chief economist at MKM Partners in Greenwich, Connecticut.
U.S. stock indexes rallied on the data, while Treasury debt prices declined slightly.
Recent data such as home sales have supported budding optimism that the worst of the 18-month recession was behind.
Initial claims are being closely watched for signs of stability in the labor market, one of the segments worst hit by the recession.
Analysts reckon new applications for unemployment benefits will have to drop below 600,000. Companies have aggressively cut their payrolls to protect costs in the face of plummeting demand.
Non-farm payrolls data for May, due for release on Friday, are expected to show U.S. employers cut 520,000 jobs that month after shedding 539,000 in April.
The number of people staying on the benefit rolls fell 15,000 to 6.74 million in the week ended May 23, the latest week for which the data is available.
This was the first time that so-called continued claims have declined since the week of January 3 and was also the first time in 17 weeks that they did not set a record. That held the insured unemployment rate at 5.0 percent for three straight weeks.
However, the four-week moving average for new claims, considered to be a better gauge of underlying trends as it irons out week-to-week volatility, rose 4,000 to 631,250 in the week ending May 30.
Steeper job cuts by companies, coupled with reduced working hours boosted productivity in the first quarter, a separate report from the Labor Department showed.
Non-farm productivity rose at a revised 1.6 percent annual rate, the fastest since the third quarter of 2008. This was well above initial estimates of a 0.8 percent increase published last month and the 0.6 percent drop in the fourth quarter.
Analysts polled by Reuters had forecast productivity, which measures the hourly output per worker, increasing at a 1.2 percent rate.
Hours worked plunged at a 9 percent annual rate in the first quarter, the largest decline since the first quarter of 1975. Hours worked in manufacturing tumbled at an annual rate of 19.5 percent, the biggest quarterly drop on records dating back to 1987.
Unit labor costs, a gauge of inflation and profit pressures closely watched by the Federal Reserve, increased 3.0 percent in the first quarter, a touch above Wall Street's estimates for a 2.9 percent advance.
(Reporting by Lucia Mutikani, Editing by Andrea Ricci)