SINGAPORE, May 26 (Reuters) - U.S. government bonds

rallied along the curve on Tuesday, as hopes for a breakthrough

deal to reopen the Strait of Hormuz had investors relaxing a bit

about the inflation outlook, ahead of a busy day of debt

auctions headlined by a two-year sale.

Two-year Treasury yields fell seven basis points

to 4.06%. Benchmark 10-year yields fell 6.4 bps to

4.51% and 30-year yields fell 5 bps to 5.03%, taking

them about 17 bps below an almost 19-year high hit last week.

Fed funds futures rallied to imply about a 56% chance of a

rate hike this year - a huge shift from the prevailing

expectation of cuts before the Iran war, but a tempering in the

outlook from just last week when pricing implied a 68% chance.

U.S. and Iranian negotiators are in Doha to discuss a

potential end to the three-month war that has choked off the

Middle East from the global oil market, lifting fuel costs and

inflation and inflation expectations around the world.

Global bond markets rallied on Monday, when the U.S. market

was closed for Memorial Day.

Analysts cautioned against the rally running further.

"First, considerable optimism on a deal may already be in

the price," said analysts at Singapore's DBS Bank.

"Second, lower oil prices also significantly reduce

recession odds. Between the paring of hawkish central bank bets

and renewed optimism on the economy, the base case for medium

term steepening remains intact."

A two-year Treasury auction and sales of shorter-dated bills

are due later in the day and investors are also on the lookout

for new Federal Reserve chair Kevin Warsh to outline his

approach.

(Reporting by Tom Westbrook; Editing by Mrigank Dhaniwala)