TREASURIES-US yields dip after data as oil prices pull back

(Updates to afternoon New York trading)

* Jobless claims rise above forecasts

* Oil prices fall on hopes for US-Iran deal

* Fed officials signal inflation as priority

By Chuck Mikolajczak

NEW YORK, June 4 (Reuters) - U.S. Treasury yields fell on Thursday after labor market data was softer than expected, while oil prices retreated on renewed hopes that a deal to end the U.S.-Israeli war with Iran could be reached. Israel and Lebanon agreed to implement a ceasefire to end hostilities, the Trump administration said on Wednesday, raising hopes for a broader agreement to end the Iran war. However, the pro-Iran Hezbollah movement rejected a new ceasefire in Lebanon on Thursday and Israel said it would not withdraw troops from the country, complicating peace efforts.

U.S. crude fell 3.1% to settle at $93.04 a barrel and Brent dropped to $95.03 per barrel, to settle down 2.84%. 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 for Friday.

TEN-YEAR TREASURY YIELD FALLS

The yield on the benchmark U.S. 10-year Treasury note slipped 2 basis points to 4.471%. 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 1.5 basis points to 4.975%.

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 42.4 basis points.

The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations for the Federal Reserve, lost 3.9 basis points to 4.045%. San Francisco Federal Reserve President Mary Daly said that the U.S. interest-rate path will depend on how the economy evolves, adding that monetary policy is "in a good place" and the Fed is prepared to respond "either way." Kansas City Federal Reserve President Jeffrey Schmid said the U.S. central bank's choice now is between being patient and holding interest rates steady or hiking rates to tamp down inflation that has been above the central bank's 2% target for years.

After beginning the year pricing in about 50 basis points of cuts from the Fed this year, market expectations have shifted and are now pricing in nearly 20 basis points in hikes, according to LSEG data.

The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities was last at 2.496% after closing at 2.527% on Wednesday, its lowest close in three months.

The 10-year TIPS breakeven rate was last at 2.378%, indicating the market sees inflation averaging about 2.4% a year for the next decade.

(Reporting by Chuck Mikolajczak, Editing by Franklin Paul, Rod Nickel)