* U.S. 10-year yield hits highest since late November

* U.S. two-year yields touch new two-week highs

* JOLTS report shows higher job openings in February

* U.S. factory orders rise

NEW YORK, April 2 (Reuters) - U.S. Treasury yields rose to multi-month highs on Tuesday, as a recent run of solid economic data reinforced expectations that the Federal Reserve could delay cutting interest rates to July or later.

The benchmark 10-year yield climbed to 4.405%, the highest since late November. It was last up 3.2 basis points (bps) at 4.361%. U.S. five-, seven- and 30-year yields also hit their highest since late November before paring gains.

U.S. two-year yields, which reflect interest rate move expectations, slipped 2.1 bps to 4.697%, after touching a fresh two-week high of 4.733%.

"This is about the prospect of fewer rate cuts this year and all the result of stronger data in the U.S.," said Thierry Albert Wizman, global rates and FX strategist at Macquarie in New York.

"(Fed Chair) Jay Powell on March 20, when he gave a dovish press conference, probably diverged a bit from where most Fed officials stood. I think most Fed officials are more cautious and more hawkish than Powell is. The market is now realizing that, with the data, the hawks - those that have been arguing for fewer than three rate cuts - are probably right."

Treasury yields earlier extended gains after data showed U.S. job openings held steady at higher levels in February, while the number of people quitting their jobs rose marginally. Job openings, a measure of labor demand, edged up 8,000 to 8.756 million, according to the monthly Job Openings and Labor Turnover Survey, or JOLTS report.

The number of workers resigning from their jobs increased 38,000 to 3.484 million in February.

A separate report showed new orders for U.S.-manufactured goods grew more than expected in February, boosted by demand for machinery and commercial aircraft. Factory orders increased 1.4%, better than expected, after dropping 3.8% in January, data showed, with economists polled by Reuters forecasting orders to rebound 1.0%.

Tuesday's reports followed a U.S. manufacturing survey on Monday which showed sector growth for the first time in 1-1/2 years in March, as production rebounded sharply and new orders increased.

Following Tuesday's data, the U.S. rate futures market has priced in a 63.5% chance of a rate cut in June, down from about 70% a week ago, the CME's FedWatch tool showed.

The market has also pared back the number of rate cuts to about two this year, from three a few weeks ago, according to LSEG's rate probability app.

Fed officials who spoke on Tuesday further reiterated that the U.S. central bank is in no rush to cut interest rates. There is a "real risk" of cutting rates too soon and locking in too-high inflation, San Francisco Fed President Mary Daly said, citing "no urgency" to adjust rates.

Cleveland Fed President Loretta Mester said she did not think the neutral rate would be as low as it was. While declining to offer a firm projection, she said the data could open the door to a June rate cut and that three rate cuts in 2024 still looks "reasonable" given the outlook, though it was a

"close call."

The yield curve steepened or narrowed its inversion, with the spread between the U.S. two- and 10-year notes at minus 33.6 bps, compared with 39.8 bps on Monday.

Tuesday's spread was the tightest in more than a week, in a so-called bear steepener scenario in which long-term interest rates rise faster than short-term ones, reflecting concerns about inflation gains that should convince the Fed to hold rates higher for longer.

(Reporting by Gertrude Chavez-Dreyfuss; Editing by Chizu Nomiyama and Nick Zieminski)