(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.