GLOBAL MARKETS-Stocks slip, with oil prices higher as war uncertainty is high

(Updates with closing market levels)

* Oil prices surge amid Strait of Hormuz shipment disruptions

* U.S. Treasury yields increase, dollar strengthens

* Euro zone growth stalls due to inflation and war impact

By Caroline Valetkevitch and Amanda Cooper

NEW YORK/LONDON, March 24 (Reuters) - Wall Street stock indexes eased on Tuesday and oil prices extended recent sharp gains as worries persisted over how long the U.S.-Israeli war on Iran will go on, even as President Donald Trump said the U.S. was talking to "the right people" in Iran to reach an agreement to end hostilities. Washington has sent a 15-point proposal to Iran aimed at ending the war in the Middle East, Reuters and other media in the U.S. and Israel reported on Tuesday after markets closed. Earlier, two people familiar with the matter told Reuters the Pentagon is expected to send thousands of soldiers from the U.S. Army's elite 82nd Airborne Division to the Middle East, adding to a big U.S. military buildup.

"There's still a lot of confusion and lack of clarity about Iran and how long the military operations will last and what the consequences for oil and global trade are. That's the key driver," said Oliver Pursche, senior vice president and advisor at Wealthspire Advisors.

"Today we're seeing a little bit more negative sentiment seep back into markets," he said.

The Dow Jones Industrial Average fell 84.41 points, or 0.18%, to 46,124.06, the S&P 500 fell 24.63 points, or 0.37%, to 6,556.37 and the Nasdaq Composite fell 184.86 points, or 0.84%, to 21,761.89.

U.S. Treasury yields added to gains after a weak auction of 2-year Treasury notes, and the dollar regained lost ground. Stocks had rallied on Monday after Trump said he had ordered the military to postpone strikes against Iranian power plants following "productive conversations" with Tehran. Iran has denied talks with the United States.

Brent futures settled higher at $104.49 a barrel. U.S. West Texas Intermediate climbed 4.79%, to $92.35.

With the war raging and shipments of about one-fifth of the world's oil and liquefied natural gas through the Strait of Hormuz curtailed, oil prices were expected to stay high.

Communication services and technology were among the day's biggest percentage declining sectors in the S&P 500.

MSCI's gauge of stocks across the globe rose 0.91 points, or 0.09%, to 985.82.

The pan-European STOXX 600 index rose 0.43%. Earlier, data showed euro zone private sector growth nearly stalled this month as inflation expectations surged and delivery times soared, adding to mounting evidence the bloc is already suffering a tangible drag from the U.S. and Israeli war on Iran. The risk of persistent inflation arising from the escalating war with Iran was strong enough to convince Fed Governor Christopher Waller to switch his support to keeping interest rates on hold from cutting them, he said last week, as market expectations for the U.S. central bank's next move shifted toward a hike in borrowing costs.

In Treasuries, the yield on benchmark U.S. 10-year notes rose 2 basis points to 4.356%, from 4.336% late on Monday. The dollar index, which measures the greenback against a basket of currencies including the yen and the euro, rose 0.06% to 99.24, with the euro down 0.09% at $1.1602. Against the Japanese yen, the dollar strengthened 0.18% to 158.72.

Spot gold rose 1.34% to $4,464.66 an ounce.

(Reporting by Caroline Valetkevitch in New York and Amanda Cooper in London; Additional reporting by Dhara Ranasinghe, in London and Rae Wee in Singapore; Editing by Arun Koyyur, Chris Reese and Lincoln Feast.)