TREASURIES-US yields higher after data as Iran talks eyed

* Job openings rose 9,000 to 7.594 million in May

* 10-yr yield set for first monthly drop in four

* Two-year yield set for fourth straight monthly climb

By Chuck Mikolajczak

NEW YORK, June 30 (Reuters) - U.S. Treasury yields were higher on Tuesday, although the benchmark 10-year note was on track to snap a three-month streak of gains, after a reading on the labor market and as investors eyed possible peace talks between the U.S. and Iran. Top U.S. envoys who have arrived in Doha will not hold a high-level meeting with Iran, a Qatari official said on Tuesday, casting doubt on the progress of efforts to bring a lasting halt to the Iran war and fully reopen the Strait of Hormuz. Yields briefly extended gains after the Labor Department said in its Job Openings and Labor Turnover Survey, or JOLTS report, that job openings, a measure of labor demand, had increased 9,000 to 7.594 million by the last day of May, above the 7.30 million estimate of economists polled by Reuters.

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

Yields have been declining in recent days until this week, 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.

"Today's number, and most critically, Thursday's number, it's really going to point a direction for the Fed," said Jack Ablin, chief investment strategist and founding partner at Cresset Capital Management in Chicago.

"I'm hopeful the jobs report on Thursday comes in kind of mildly positive, that would be best result. But if we get another strong result like this we could see Fed tightening expectations really ratchet up."

TREASURY YIELDS ADVANCE

The yield on the benchmark U.S. 10-year Treasury note rose 2.6 basis points to 4.4%. Despite the monthly decline, the yield was set for its third-straight quarterly advance.

U.S. markets are closed on Friday for the July 4 Independence Day holiday. The yield on the 30-year bond rose 2.5 basis points to 4.885% and was also on track to snap a three-month streak of gains and a slight decline for the quarter. 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 26.7 basis points. The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations for the Fed, rose 2.2 basis points to 4.131% and was on track for a fourth straight monthly gain, its longest since early 2022 and second straight quarterly gain. Markets are pricing in a 31.5% chance for a rate hike of at least 25 basis points at the Fed's July meeting, and a 67% at the September meeting, according to CME FedWatch. The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities was last at 2.278% after closing at 2.249% on June 29. The 10-year TIPS breakeven rate was last at 2.241%, indicating the market sees inflation averaging about 2.2% a year for the next decade.

(Reporting by Chuck Mikolajczak Editing by Nick Zieminski)