By Chuck Mikolajczak

NEW YORK, July 2 (Reuters) - U.S. Treasury yields declined on Thursday, after a weaker-than-expected report on the labor market dented expectations for a rate hike by the Federal Reserve in the near future.

The Labor Department said nonfarm payrolls increased by 57,000 jobs last month after a downwardly revised 129,000 rise in May, well below the 110,000 estimate of economists polled by Reuters and the previously reported 172,000 in May.

Expectations for a rate hike from the Fed decreased in the wake of the report, with markets pricing in a 19.8% chance for a hike of at least 25 basis points at its July meeting, according to CME FedWatch, down from 28.9% in the prior session. For the September meeting, hike expectations dimmed to 55% from 64.1%.

"What it tells us, both today's number, but especially in conjunction with the revision downward of last month's number, is that the labor market was never as hot as last month suggested, and today is weaker than expected, but when you look at the moving average, it's still okay," said Ellen Hazen, chief market strategist at F.L.Putnam Investment Management in Lynnfield, Massachusetts.

"It buys (Fed Chairman) Warsh some time. So it takes the pressure off. Because they made it clear that they were focusing on inflation more than the labor market."

TREASURY YIELDS DECLINE

The yield on the benchmark U.S. 10-year Treasury note US10YT=TWEB fell 0.2 basis point to 4.473% after earlier climbing to 4.051%, its highest since June 23. The yield is up about 10 basis points on the week, on track to snap a three-week run of declines and biggest weekly gain since mid-May.

Other data from the labor market showed weekly initial jobless claims of 215,000, below the 220,000 estimate and a slight decline from the upwardly revised 216,000 in the prior week.

The yield on the 30-year bond US30YT=TWEB rose 1.5 basis points to 4.981% after climbing to 4.9976%, its highest since June 11. The yield is up about 12 basis points on the week, which would mark its first weekly gain in four, and largest since mid-May.

CENTRAL BANK POLICY OUTLOOK

Several Fed officials have flagged concerns about inflation pressures in recent weeks.

However, San Francisco Federal Reserve President Mary Daly said on Thursday that U.S. monetary policy is "slightly restrictive" but that with "exceedingly strong" investment growth in AI-related technology and a stable labor market it's unclear what the Fed's next step should be.

A closely watched part of the U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes US2US10=TWEB, seen as an indicator of economic expectations, was at a positive 35.3 basis points.

The two-year US2YT=TWEB U.S. Treasury yield, which typically moves in step with interest rate expectations for the Fed, fell 4.6 basis points to 4.118% and was on track to snap a three-day streak of gains. The yield is up about 4 basis points on the week.

The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) US5YTIP=TWEB was last at 2.254% after closing at 2.259% on Wednesday.

The 10-year TIPS breakeven rate US10YTIP=TWEB was last at 2.229%, indicating the market sees inflation averaging about 2.2% a year for the next decade.