TREASURIES-US bonds in holding pattern on uncertain US-Iran outlook

(Adds fresh analyst comment, Trump's remarks from press briefing, yield curve; updates yields)

* Middle East ceasefire plan proposes immediate truce

* Shifting comments by Trump, Iran add to market uncertainty

* US services sector cools, but prices paid index surge

* US rate futures price out rate cuts in 2026

By Gertrude Chavez-Dreyfuss

NEW YORK, April 6 (Reuters) - U.S. Treasuries were little changed on Monday as bond investors were caught between optimism over reports of a ceasefire plan for the Middle East and unease over President Donald Trump's threat to escalate strikes on Iran if it does not reopen the vital Strait of Hormuz.

Volume was generally thin, with European and some Asian markets closed for the Easter holiday. In afternoon trading, the benchmark 10-year yield, which falls when Treasury prices rise, was down 1.1 basis points at 4.335% US10YT=RR. Last week, the yield posted its largest weekly drop since February 23.

On the shorter end of the curve, the two-year yield, which reflects interest-rate expectations, was flat at 3.850% . It had its biggest weekly fall last week since late February. Trump said on Monday that opening the Hormuz Strait was a big priority and repeated his threats to rain "hell" on Iran if it does not make a deal by 8 p.m. EDT Tuesday (midnight GMT) to open the waterway through which about a fifth of global oil and liquefied natural gas typically passes. A Pakistani-brokered plan emerged from intense overnight contacts, and it proposes an immediate ceasefire followed by negotiations on a broader peace settlement to be concluded within 15 to 20 days, a source aware of the proposals said on Monday. Iran rejected the ceasefire, and said it wants an end to the war.

"There's no specific direction for the bond market at this point, and that's telling me that investors don't really know," said Jim Barnes, director of fixed income at Bryn Mawr Trust in Berwyn, Pennsylvania. "There's a lot of headline risk about deadlines. And it's very difficult for investors to try to trade on what could happen down the road because we have been down this road before where we had these ultimatums."

DARING RESCUE The ceasefire proposal followed a weekend rescue of a crew member of a U.S. fighter jet who had been stranded in Iran since Thursday after his aircraft was shot down. The pilot was rescued in a separate operation carried out on Thursday.

U.S. crude futures were modestly higher on the day, up 0.7% at $112.29 per barrel, while stocks climbed, with the Nasdaq Composite up the most. In other Treasury maturities, U.S. 30-year yields were last 1.7 bps lower at 4.889% US30YT=RR. The long bond yield last week had its biggest weekly slide since late February.

The yield curve flattened on Monday, with the gap between two-year and 10-year yields at 48.5 bps, compared with 50.5 bps late on Thursday.

The curve showed a bull-flattening move as a result of long-term yields falling faster than those on the short end. It is a scenario that has taken place for three straight sessions, and it suggests that investors are still pricing in policy easing from the Fed due to mounting worries about growth triggered by the Iran war. Treasuries, meanwhile, showed little reaction to a report that U.S. services sector growth slowed in March, while businesses' input costs hit a near 3-1/2-year high, likely an indication that the Iran war is boosting inflation pressures. A stronger-than-expected U.S. payrolls report for March last Friday triggered a selloff in Treasuries, lifting their yields higher. The data cemented expectations that the Federal Reserve will hold interest rates steady for longer even in the midst of an easing cycle.

On Monday, U.S. rate futures priced out rate cuts this year, compared with about 55 basis points of easing before the Iran war began on February 28.

(Reporting by Gertrude Chavez-Dreyfuss; Editing by Susan Fenton and Will Dunham)