TREASURIES-US bonds rally on hope Strait deal cools inflation

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)