TREASURIES-US yields lower after data as oil prices ease

* US job openings surge to 7.618 million in April, exceeding forecasts

* Cleveland Fed's Hammack warns inflation pressures may require action soon

* Oil prices subdued on report Iran reviewing agreement

By Chuck Mikolajczak

NEW YORK, June 2 (Reuters) - U.S. Treasury yields dipped on Tuesday, after a reading on the labor market showed a jump in job openings and as crude oil prices were little changed after a jump the day prior. Iran is reviewing a proposed agreement with the U.S. to halt the war, Iranian media reported, after U.S. President Donald Trump said talks to reach a deal were continuing. Yields had climbed on Monday after a report that Tehran's negotiating team was stopping exchanges of messages with the United States through mediators, which caused crude oil prices to surge. U.S. crude edged up 0.12% to $92.27 a barrel and Brent rose to $95.27 per barrel, up 0.31% on the day.

JOB OPENINGS SURGE Yields pared declines after the Labor Department said in its Job Openings and Labor Turnover Survey, or JOLTS report, that job openings surged 731,000 to 7.618 million by the last day of April, the highest level since May 2024, and well above the 6.88 million forecast of economists polled by Reuters.

"Are we finally exiting the 'no hire, no fire' mire? Possibly. Job openings surged in April," said Brian Jacobsen, chief economist at Annex Wealth Management in Menomonee Falls, Wisconsin.

"People still aren't quitting and layoffs are low, but the tide could be turning for the labor market."

The data is the first in a string of reports on the labor market this week, culminating in Friday's key government payrolls report.

The yield on the benchmark U.S. 10-year Treasury note fell 2.8 basis points to 4.449%. After hitting a 16-month high of 4.687% on May 19, the yield has been declining on optimism that a peace deal between the U.S. and Iran could be reached.

The yield on the 30-year bond shed 3 basis points to 4.961%. Federal Reserve Bank of Cleveland President Beth Hammack said the U.S. central bank may need to act "soon" to combat inflation pressures that are already too high and are on a worrisome trend.

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 40.6 basis points.

The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations for the Fed, fell 1.4 basis points to 4.037%. After beginning the year pricing in roughly 50 basis points worth of cuts from the Fed this year, market expectations have shifted to price in a slight possibility of a rate hike. Expectations for a hike of at least 25 basis points at the central bank's December meeting currently stand at roughly 50%, according to CME FedWatch, up from 9.3% a month ago.

The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) was last at 2.549% after closing at 2.544% on Monday.

The 10-year TIPS breakeven rate was last at 2.406%, indicating the market sees inflation averaging about 2.4% a year for the next decade.

(Reporting by Chuck Mikolajczak; Editing by Andrea Ricci )