* 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.