Updates prices and commentary

By Chuck Mikolajczak

NEW YORK, June 29 (Reuters) - U.S. Treasury yields edged higher on Monday, as crude prices rose following attacks between the U.S. and Iran over the weekend and ahead of a flurry of labor market data later this week.

U.S. crude CLc1 rose 2.02% to $70.62 a barrel and Brent LCOc1 rose to $72.92 per barrel, up 1.29% on the day as the attacks once again threatened a tenuous peace deal, although expectations of a continued recovery in energy shipping through the Strait of Hormuz kept gains in check.

Iranian and U.S. technical teams working on the implementation of an interim peace deal are expected to meet in Doha in the coming days, a source told Reuters on Monday.

Markets will see a string of data on the labor market this week, culminating with the release on Thursday of the Labor Department's monthly payrolls report for June.

Markets are closed on Friday for the U.S. Independence Day holiday on July 4.

Yields have been declining in recent days as expectations of easing inflation pressures have grown with a decline in oil prices, offsetting what was seen as a hawkish Federal Reserve policy announcement and press conference by new Fed Chairman Kevin Warsh on June 17.

"The labor market to me is really interesting, the data for this week, but the key, the focus now is more on the inflation side," said Jim Barnes, director of fixed income at Bryn Mawr Trust.

"Because energy prices have materially come down, inflation expectations have notably come down. But the market now, especially after the Fed meeting, it's not good enough, now they have to start to see more concrete evidence that inflation's coming down."

BENCHMARK YIELDS EDGE HIGHER

The yield on the benchmark U.S. 10-year Treasury note US10YT=TWEB edged up 0.6 basis point to 4.378% after having fallen for three straight weeks.

Comments from several Fed officials indicated last week that they were still concerned about high inflation.

The yield on the 30-year bond US30YT=TWEB shed 0.3 basis point to 4.862%.

Barclays analysts on Monday said in a note that AI-related categories have been putting upward pressure on inflation as measured by the personal consumption expenditures price index (PCE) and while price gains may moderate as supply increases, "the Fed will likely find it hard to dismiss AI-related inflation entirely."

Markets are currently pricing in a 31.5% chance of a rate hike of at least 25 basis points at the Fed's July 28-29 meeting, according to CME Group's FedWatch tool, and a 62.9% chance at the September 15-16 meeting.

The two-year US2YT=TWEB U.S. Treasury yield, which typically moves in step with interest rate expectations for the Fed, rose 2.5 basis points to 4.113% and was on track for its first daily gain after four straight declines.

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 26.1 basis points.

The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) US5YTIP=TWEB was last at 2.256% after closing at 2.223% on Friday.

The 10-year TIPS breakeven rate US10YTIP=TWEB was last at 2.224%, indicating the market sees inflation averaging about 2.2% a year for the next decade.