(Updated at 1500 EDT/1900 GMT)

By Karen Brettell

June 6 (Reuters) - Benchmark U.S. 10-year Treasury

yields dipped on Thursday as investors waited to see if Friday's

employment report for May will show cooling in the labor market

as traders bet on Federal Reserve rate hikes later this year.

Bonds have rallied this week as investors price for the

likelihood that the Fed could begin cutting rates as soon as

September as the economy softens.

Inflation easing closer to the U.S. central bank's 2% annual

target is key to when the Fed cuts and how many rate reductions

are likely this year.

"The next month or two in terms of data is going to be very,

very telling," said Scott McIntyre, senior portfolio manager at

HilltopSecurities Asset Management in Austin, Texas.

"We're at this pivot point where investors are wondering

whether the hot first quarter numbers are going to cool in the

second quarter," McIntyre said. "We're just now getting numbers

for May so that hasn't been determined yet."

Benchmark 10-year note yields were last down 1

basis point on the day at 4.281%. They got as low as 4.275% on

Wednesday, the lowest since April 1.

Two-year note yields dipped 1 basis point to

4.720% and got as low as 4.718%, the lowest since May 16.

The inversion in the two-year, 10-year yield curve

narrowed 1 basis point to minus 44 basis points.

Traders said that the absence of fresh Treasury supply had

supported the market this week after some soft bond auctions

last week.

However, investors have also positioned for softer jobs data

on Friday, with the possibility that jobs gains will come in

below the median economist forecast of 185,000 jobs.

April's report showed that jobs growth slowed more than

expected, with 175,000 jobs gains, the fewest in six months.

Economists at Goldman Sachs said on Thursday that they

expect 160,000 job additions in May.

"When the labor market is tight, job growth tends to slow

disproportionately during the spring hiring season and

particularly in May - when the seasonal factors expect more

hiring than is realistic with fewer workers available," they

said in a report.

Data this week has pointed to more balance in the labor

market.

The ADP Employment Report on Wednesday showed that private

payrolls increased by 152,000 jobs last month, below economists'

forecasts for 175,000 in jobs gains.

A survey on Tuesday also showed that job openings, a measure

of labor demand, were down 296,000 to 8.059 million on the last

day of April, the lowest level since February 2021.

Data on Thursday showed that the number of Americans filing

new claims for unemployment benefits increased last week. U.S.

worker productivity also grew slightly less than previously

estimated in the first quarter but exceeded market expectations,

and unit labor costs rose by less than first thought.

Wage data in Friday's jobs report will be closely watched as

inflation remains the key focus for Fed policy.

"Average hourly earnings realistically are probably the most

important component, I think, because that feeds into inflation,

and inflation right now is priority one for the Fed," McIntyre

said.

Next week's consumer price index (CPI) report for May will

then be key to guiding near-term Fed expectations. Fed officials

have stressed that they want to see several months of improving

inflation before easing policy.

The consumer price inflation report will come on Wednesday,

before the U.S. central bank is due to complete a two-day policy

meeting at which Fed officials will update their economic and

interest rate projections.