TREASURIES-Yields ease as oil trims gains, Trump touts Iran war progress

* Oil prices surge to over $119 a barrel amid supply cuts

* Fed funds futures show 77% odds of rate cut in July

* Treasury to auction $119 billion in coupon-bearing debt this week (Updated in New York afternoon time)

By Karen Brettell

NEW YORK, March 9 (Reuters) - U.S. Treasury yields eased on Monday after oil prices trimmed their earlier surge and President Donald Trump said the U.S. is "very far" ahead of his initial four- to five-week estimated time frame for the war in Iran. Brent crude futures were last up 2.3% at $95 a barrel after earlier reaching more than $119 a barrel, the highest since mid-2022. The spike came as some major producers cut supplies and fears of prolonged shipping disruption gripped the market due to the expanding U.S.-Israeli war with Iran.

"Oil is driving most of this move," said Tom di Galoma, managing director at Mischler Financial Group.

Trump also said that "I think the (Iran) war is very complete, pretty much," according to a CBS reporter on X.

Both two-year and 10-year yields last week saw their biggest weekly yield increase since last April's tariff turmoil on rising concerns over how long the conflict with Iran will last. Iran's hardliners staged a show of force on Monday, taking to the streets to proclaim their loyalty to new Supreme Leader Mojtaba Khamenei, whose rise appeared to dash hopes of a swift end to war in the Middle East.

Treasuries have also followed sharp yield increases and the yield-curve flattening in Europe, di Galoma said, noting reports that hedge funds were being forced to exit losing positions.

The yield on the two-year note was last down 0.4 basis points at 3.552%. It earlier reached 3.635%, the highest since November 20.

The benchmark U.S. 10-year note yield fell 3 basis points to 4.102% after earlier trading at 4.216%, the highest since February 9.

The yield curve between two- and 10-year notes flattened by around 2 basis points to 55 basis points.

Fed funds futures are now pricing in 77% odds of a rate cut in July, up from 67% earlier on Monday and are fully pricing in a reduction in September.

They are pricing in 42 basis points of cuts by year-end, indicating some doubts over whether the U.S. central bank will make a second 25-basis-point cut this year.

A prolonged oil price increase would likely slow the economy, which could then lead traders to reevaluate and price in more rate cuts.

"Investors reacted to recent events in Iran by placing more weight on upside risks to inflation than downside risks to growth, sending Treasury yields higher," Morgan Stanley rates strategists led by Martin Tobias said in a report.

"After the February jobs report, we think investors will have little trouble shifting focus toward downside growth risks each day this exogenous shock persists," they added. Yields briefly fell on Friday after data showed that the U.S. economy unexpectedly lost jobs in February. Nonfarm payrolls decreased by 92,000 jobs last month, while the unemployment rate rose to 4.4%. Demand for Treasuries will be tested this week with $119 billion in coupon-bearing debt auctions.These will include $58 billion in three-year notes on Tuesday, $39 billion in 10-year notes on Wednesday, and $22 billion in 30-year bonds on Thursday.

(Reporting by Karen Brettell; Editing by Pooja Desai, Nick Zieminski and Deepa Babington)