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

(Updates yields, adds results of 2-year auction, economic indicators in paragraphs 1-2, 6, 8-12)

WASHINGTON, May 26 (Reuters) - Yields on U.S. government bonds held to lower levelson Tuesday, as hopes for a breakthrough deal to reopen the Strait of Hormuz had investors relaxing a bit about the inflation outlook at the start of a holiday-shortened week featuring major U.S. economic data releases.

A $69 billion auction of two-year notes showed solid investor appetite, with slightly higher-than-average demand for the debt at 2.64 times the notes on sale. U.S. President Donald Trump on Monday signaled negotiations to end the conflict with Iran were proceeding "nicely." However, Tehran later accused the U.S. of a "gross violation" of the current ceasefire after Washington conducted what it 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 have been meeting in Doha to discuss a potential end to the three-month war that has constrained the global oil market, lifting fuel costs and inflation around the world. U.S. Secretary of State Marco Rubio said on Tuesday reaching an agreement could take "a couple of days."

Data released on Tuesday showed gains in the S&P Cotality Case-Shiller indices fell short of expectations. A measure of consumer confidence came in higher than expected while edging lower. The data left markets largely unmoved.

The U.S. later this week is due to publish GDP, inflation, durable goods and trade data.

The yield on the benchmark U.S. 10-year Treasury note fell 8.1 basis points to 4.491%. The yield on the 30-year bond fell 5.9 basis points to 5.023%.

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 44.2 basis points.

The two-year U.S. Treasury yield, which typically moves in step with interest rate expectations for the Federal Reserve, fell 8 basis points to 4.047%.

The breakeven rate on five-year U.S. Treasury Inflation-Protected Securities (TIPS) was last at 2.536% after closing at 2.538% on May 22.

The 10-year TIPS breakeven rate was last at 2.412%, indicating the market sees inflation averaging about 2.4% a year for the next decade. (Reporting by Douglas Gillison; Editing by Mrigank Dhaniwala, Nick Zieminski and Paul Simao)