(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.