TREASURIES-Bonds climb as jobs worries stoke safety bid

* Bonds rise on data showing grim labor market

* Plunging stocks also stoke safety bid for bonds

* Risks seen to downside in Friday's payrolls report (Adds economist's quotes, updates prices)

By Chris Reese

NEW YORK, Sept 4 (Reuters) - U.S. Treasury debt prices rose on Thursday, taking benchmark yields to four-month lows as plunging stocks stoked a safety bid for government debt on more signs of deterioration in the labor market.

Data released on Thursday showed a surprise rise in weekly jobless claims, a bigger-than-forecast contraction in private employment in August, and continued shrinking of employment activity in the services sector last month.

Bonds were also supported by data showing unit labor costs, a gauge of inflation and profit pressures that are closely watched by the Federal Reserve, unexpectedly contracted in the second quarter.

"The data we have seen so far has been relatively bond friendly," said Kim Rupert, managing director of global fixed income analysis at Action Economics LLC in San Francisco, adding "the fact that you continue to see declines in jobs is bullish for Treasuries."

The benchmark 10-year note US10YT=RR rose 10/32 in price for a yield of 3.66 percent, the lowest since mid-April, from 3.70 percent late on Wednesday. Two-year Treasuries rose 2/32 for a yield of 2.23 percent from 2.27 percent.

The Labor Department said initial claims for state unemployment insurance benefits climbed to a seasonally adjusted 444,000 in the week ended Aug. 30 from a revised 429,000 in the prior week. Analysts had been looking for a reading of 425,000. For details see [ID:nN04523535].

Also on Thursday, ADP Employer Services said U.S. private employers cut 33,000 jobs in August, compared with forecasts of a fall of 30,000.

While the Institute for Supply Management's services index showed unexpected expansion in the sector last month, the employment activity component showed contraction for the seventh time in the last eight months.

"This report does post a rise in the index this month, but it is not a good report and it is a weak report ... for jobs," said Robert Brusca, chief economist at Fact and Opinion Economics in New York.

Analysts said the news on the labor market skewed risks to the downside on forecasts for Friday's all-important data on August nonfarm payrolls.

Economists' median forecast is for U.S. nonfarm payroll jobs to have fallen by 75,000 in August, which would be the eighth straight month of job losses. If Friday's jobs report deepens the impression that the labor market is slipping, that should continue to add to demand for government debt.

Also on Thursday the Labor Department reported that U.S. business productivity surged at a revised annual rate of 4.3 percent, much stronger than the 3.5 percent rate forecast by economists.