* Jobless claims rise above forecasts

* Oil prices fall on hopes for US-Iran deal and

Israel-Lebanon ceasefire

* Fed's Lorie Logan says policy may be too loose

By Chuck Mikolajczak

NEW YORK, June 4 (Reuters) - U.S. Treasury yields were

lower on Thursday, after labor market data was softer than

expected, while oil prices tumbled on renewed optimism a deal to

end the war between the U.S. and Iran could be reached.

Israel and Lebanon agreed to implement a ceasefire to end

hostilities, the Trump administration said on Wednesday,

increasing hopes for progress on a broader agreement to end the

U.S.-Israeli war on Iran.

U.S. crude fell 3.27% to $92.88 a barrel and Brent

dropped to $95.12 per barrel, down 2.75% on the day.

On the economic front, the Labor Department said weekly initial

jobless claims rose 13,000 to a seasonally adjusted 225,000,

topping the 213,000 estimate of economists polled by Reuters,

although the underlying trend indicated the labor market was on

stable footing.

"If we get a deal done, then we'll have a short-run

reprieve," said Thomas Urano, co-chief investment officer at

Sage Advisory in Austin.

"The background is we know we've got inflation pressure

that's still there and pretty constant... and the only other

ballast that we've had so far has been the idea of a weak labor

market."

The claims data was the latest in a string of reports on the

labor market this week, with the key government payrolls report

scheduled to be released on Friday.

TEN-YEAR TREASURY YIELD FALLS

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

fell 4 basis points and was on track for its

biggest daily drop since May 26, to 4.451%.

Other data from the Labor Department showed worker productivity

increased at a downwardly revised 0.3% annualized rate last

quarter, the slowest pace since the first quarter of 2025 and

shy of the 0.5% estimate.

Unit labor costs increased at a 1.8% rate last quarter, a

downward revision from the 2.3% pace reported last month and

below the 2.5% forecast.

The yield on the 30-year bond declined 2.6 basis

points to 4.963%.

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 42.2 basis points.

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

moves in step with interest rate expectations for the Federal

Reserve, dropped 5.7 basis points to 4.027%.

Federal Reserve Bank of Dallas President Lorie Logan said late

on Wednesday that she feels monetary policy is currently

"neutral or perhaps even a bit loose," and needs to be "at least

mildly restrictive" to get inflation down to its 2% target.

After beginning the year pricing in about 50 basis points

worth of cuts from the Fed this year, market expectations have

shifted and are now pricing in roughly 20 basis points in hikes,

according to LSEG data.

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

Inflation-Protected Securities (TIPS) was last at

2.488% after closing at 2.527% on Wednesday, its lowest close in

three months.

The 10-year TIPS breakeven rate was last at

2.365%, indicating the market sees inflation averaging about

2.4% a year for the next decade.