TREASURIES-Yields edge higher on Iran tensions, core CPI cools

(Updated in New York afternoon time)

* Trump warns Iran, oil prices rise

* Core CPI rose less than expected

* Futures pricing in 65% odds of Fed hike by December

By Karen Brettell

NEW YORK, June 10 (Reuters) - U.S. Treasury yields edged up on Wednesday on rising tensions between the United States and Iran after data earlier showed core consumer price inflation eased more than economists had expected last month. U.S. President Donald Trump said on Wednesday Iran had taken too long to negotiate a deal and would now "have to pay the price." Iran said it would reassess diplomatic engagement with the United States after overnight tit-for-tat strikes.

The exchange of fire, which came after Trump said Iran had downed a U.S. Apache helicopter near the strait, marks one of the most significant escalations since the two countries agreed to a ceasefire in April in the war that began in February. Traders are keeping an eye on oil prices, which gained on the news, as the Iran war drags on, even as many traders continue to be optimistic that a deal to end the hostilities will be reached.

The 2-year note yield, which typically moves in step with Fed interest rate expectations, was last flat on the day at 4.125%.

The yield on benchmark U.S. 10-year notes rose 1.2 basis points to 4.54%.

The yield curve between 2- and 10-year notes steepened to 41.4 basis points.

Yields fell earlier on Wednesday after data showed that core inflation in May was slightly softer than expected. The consumer price index rose 0.5% in May, putting the annual inflation rate at 4.2% - the highest level since April 2023 and above the 3.8% reading from April.

Stripping out volatile food and energy prices, the core CPI rose 0.2% for the month and 2.9% from a year ago - below the 0.3% monthly estimate and less than the 0.4% April increase.

"Some relief was expected in the core inflation number (Wednesday) morning, and this report mostly delivered that relief," said Matt Bush, U.S. economist at Guggenheim Investments.

The data showed that the effects of tariffs on prices continued to fall while technology-related inflation eased. Services prices, however, remained elevated, with higher energy costs feeding through to airfares, Bush said.

Rental inflation also moderated, but less than some analysts had expected, indicating likely further progress in the months ahead.

"Some good news in the data, still some areas to be worried about," Bush said. "Overall, probably has not much bearing on the near-term path of Fed policy."

Fed funds futures traders are pricing in 65% odds of a Federal Reserve hike by December, little changed from Tuesday.

The Treasury saw good demand for a $39 billion sale of 10-year notes later on Wednesday, the second sale of $119 billion in coupon-bearing supply this week. The debt sold at a high yield of 4.538%, a fraction of a basis point below where it traded before the sale. Demand was 2.57 times the amount of debt on offer, the highest since September.

The U.S. government saw average demand for a $58 billion sale of three-year notes on Tuesday. It will also sell $22 billion in 30-year bonds on Thursday.

(Reporting by Karen Brettell; Editing by Will Dunham)