TREASURIES-US yields fall on hope Strait of Hormuz deal can cool inflation

(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. (Reporting by Tom Westbrook; Editing by Mrigank Dhaniwala and Nick Zieminski)