* June CPI rose 3.5% on year-over-year basis, down 0.4% on

the month

* July rate hike odds fell to 13.4% from 41.7%, CME Group's

FedWatch tool showed

* Fed's Warsh says central bank has no tolerance for

inflation

By Chuck Mikolajczak

NEW YORK, July 14 (Reuters) - U.S. Treasury yields fell on

Tuesday after data showed consumer inflation slowed more than

expected in June, denting market expectations for a near-term

rate hike from the Federal Reserve.

The Labor Department said the Consumer Price Index increased

3.5% in the 12 months through June after surging 4.2% in May,

the largest year-on-year rise since April 2023. On a monthly

basis, CPI fell 0.4% after a 0.5% increase in May. Economists

polled by Reuters had forecast the CPI would rise 3.8% on a

year-over-year basis and dip 0.1% on a monthly basis.

"The more important thing for consumer sentiment is that

energy number. Regular unleaded gasoline prices were still up

more than 27% from a year ago even with the 10% drop in prices

in June," said Brian Jacobsen, chief economist at Annex Wealth

Management in Menomonee Falls, Wisconsin.

"Headline CPI is hot, but it's not rotten to the core."

The yield on the benchmark U.S. 10-year Treasury note

fell 3.7 basis points, on pace for its biggest

daily drop since June 24, to 4.573%, after falling to 4.526%.

CRUDE CLIMBS ON MIDDLE EAST CONCERNS

Energy prices have come down in recent weeks on expectations

that a durable peace deal could be reached between the U.S. and

Iran. However, hostilities have intensified in recent days and

caused a reversal in crude prices.

U.S. crude rose 3.28% to $80.70 a barrel and Brent

climbed to $86.91 per barrel, up 4.35% on the day. The

two benchmarks touched four-week highs after the U.S. reimposed

a naval blockade of Iran and as renewed attacks between

Washington and Tehran exacerbated supply concerns.

The yield on the 30-year bond shed 0.7 basis

point to 5.091% after dropping to 5.05%.

Expectations for a rate hike of at least 25 basis points from

the Fed at its July 28-29 meeting tumbled to 13.4% from 41.7% in

the prior session, according to CME Group's FedWatch tool. For

the central bank's September 15-16 meeting, markets are pricing

in a 58.1% chance of a hike, down from 75.1% on Monday.

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 38 basis points.

Several Fed officials have in recent weeks flagged concerns

about inflation pressures while playing down any labor market

worries. On Monday, Federal Reserve Governor Christopher Waller

said the central bank may need to raise interest rates "in the

near term" if coming data show inflation continuing well above

the central bank's 2% target.

Fed Chairman Kevin Warsh said in prepared comments on Tuesday to

the U.S. House of Representatives Financial Services Committee

that the central bank "has no tolerance for persistently

elevated inflation."

The two-year U.S. Treasury yield, which

typically moves in step with interest rate expectations for the

Fed, fell 7.2 basis points to 4.191% after dropping to 4.147%,

and was on track for its biggest daily decline since May 26.

The breakeven rate on five-year U.S. Treasury

Inflation-Protected Securities (TIPS) was last at

2.259% after closing at 2.329% on July 13.

The 10-year TIPS breakeven rate was last at

2.239%, indicating the market sees inflation averaging about

2.2% a year for the next decade.