TREASURIES-US Treasury yields decline as Iran ceasefire holds, oil prices fall

* Crude prices drop but remain volatile after recent Middle East tensions

* Job openings fall but above expectations

* ISM Services expansion slows for second straight month (Updates to afternoon New York trading)

By Chuck Mikolajczak

NEW YORK, May 5 (Reuters) - U.S. Treasury yields fell on Tuesday, along with a decline in crude prices as there were no fresh signs of escalation in the U.S.-Iran war, offering a respite to recent inflation worries while investors assessed a batch of economic data.

Washington said a shaky ceasefire was intact despite an exchange of fire the previous day as U.S. forces attempted to force open the Strait of Hormuz. However, the United Arab Emirates said it was under attack from Iranian missiles and drones. U.S. crude fell 3.68% to $102.54 a barrel and Brent fell to $110.35 per barrel, down 3.6% on the day, as tensions remained unresolved.

Since the U.S.-Israeli war with Iran began at the end of February, yields have steadily climbed as worries about higher prices have dented market expectations for rate cuts from the Federal Reserve this year.

"There's not enough big headlines really to move it too much in one direction or another, we're still at levels we didn't contemplate at the beginning of the year, before the U.S.-Iran conflict, for sure," said JoAnne Bianco, partner and senior investment strategist at BondBloxx Investment Management in Chicago.

"It's a really big move since the beginning of March, so we're just at a more elevated level. It seems like the odds are that if we continue to have Brent crude go up $3 to $5 a day, you can see our rates (rise), but that's also starting to make fixed income more attractive, especially in the intermediate part of the curve." The yield on the benchmark U.S. 10-year Treasury note fell 3 basis points to 4.416% after rising to 4.464% on Monday, its highest since March 27. Several brokerages have scaled back expectations for rate cuts from the Federal Reserve since the start of the year, when markets were pricing in about 50 basis points of cuts for 2026. The yield on the 30-year bond lost 4 basis points to 4.985% after breaching the 5% level to hit 5.036% on Monday, its highest since July 17.

Markets will receive several reports on the health of the labor market this week, culminating in the government's jobs report on Friday. Economists polled by Reuters forecast a 62,000 rise in nonfarm payrolls. Data from the Labor Department on Tuesday showed job openings were down 56,000 to 6.866 million in March but above the 6.835 million forecast of economists polled by Reuters.

A separate survey from the Institute for Supply Management said its nonmanufacturing purchasing managers index dropped to 53.6 last month from 54.0 in March and slightly below the 53.7 estimate. A reading above 50 indicates expansion and this was the second consecutive month that expansion has slowed.

A closely watched part of the U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes, seen as an indicator of economic expectations, was at a positive 47.6 basis points. The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations for the Fed, dipped 2.4 basis points to 3.938% after hitting 3.993% on Monday, its highest since March 27.

The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) was last at 2.768% after closing at 2.828% on Monday, its highest close since August 2022.

The 10-year TIPS breakeven rate was last at 2.482%, indicating the market sees inflation averaging about 2.5% a year for the next decade.

(Reporting by Chuck Mikolajczak, editing by Deepa Babington and Nick Zieminski)