(Updates yields, adds latest developments, expected government

data releases, fresh comment in paragraphs 2-3 and 6-12)

WASHINGTON, May 26 (Reuters) - Yields on U.S. government

bonds fell 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.

U.S. President Donald Trump on Monday had signaled

negotiations to end the conflict with Iran were proceeding

"nicely." However, Tehran later accused the United States of a

"gross violation" of the current ceasefire after U.S. forces

conducted what Washington called defensive strikes in southern

Iran.

"Markets seem to think that a deal is close at hand. As long

as there's optimism around a deal, that's creating a stronger

backdrop," said Gennadiy Goldberg, head of U.S. rates strategy

at TD Securities. "It's potentially premature. We've seen a lot

of twists and turns."

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. U.S. Secretary of State

Marco Rubio said Tuesday that reaching an agreement could take

"a couple of days."

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

was closed for Memorial Day.

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

due later in the day. From Thursday to Friday, the United States

is also due to publish data on first-quarter economic growth, as

well as April data on inflation, durable goods orders and the

U.S. trade balance.

Markets were also eyeing Tuesday's release of May consumer

confidence data but were largely unmoved after March gains in

the S&P CaseShiller index fell short of expectations.

The yield on the benchmark U.S. 10-year Treasury note

was last down 8.7 basis points to 4.485%, its

lowest level in nearly two weeks. The yield on the 30-year bond

fell 6.9 basis points to 5.013%.

A closely watched part of the U.S. Treasury yield curve

measuring the gap between yields on two- and 10-year Treasury

notes, seen as an indicator of economic

expectations, was at a positive 43.0 basis points.

The two-year U.S. Treasury yield, which

typically moves in step with interest rate expectations for the

Fed, fell 7.6 basis points to 4.051%.

The breakeven rate on five-year U.S. Treasury

Inflation-Protected Securities (TIPS) was last at

2.514% after closing at 2.538% on May 22.

The 10-year TIPS breakeven rate was last at

2.389%, indicating the market sees inflation averaging about

2.4% a year for the next decade.