GLOBAL MARKETS-Stocks mixed, with oil prices higher as war uncertainty remains

* 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

(Updates to late morning New York time)

By Caroline Valetkevitch

NEW YORK/LONDON, March 24 (Reuters) - Major global stock indexes were mixed on Tuesday as oil prices extended recent sharp gains and worries persisted over how long the Israeli-U.S. war on Iran will go on.

U.S. Treasury yields pushed higher and the dollar regained lost ground.

Stocks had rallied on Monday after U.S. President Donald 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.

Oil prices rose on Tuesday. U.S. crude gained 3.63% to $91.33 a barrel and Brent rose to $98.54.

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.

"Today we're seeing a little bit more negative sentiment seep back into markets," said Oliver Pursche, senior vice president and advisor at Wealthspire Advisors. "Investors are mostly focused on oil prices, but to me the bigger risk is commodity-related inflation, in particular related to agriculture ... That could have a much more profound, longer-term impact than oil prices."

Also, he said, "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."

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

The Dow Jones Industrial Average rose 145.83 points, or 0.30%, to 46,348.22, the S&P 500 rose 5.77 points, or 0.09%, to 6,586.74 and the Nasdaq Composite fell 70.12 points, or 0.32%, to 21,877.14.

MSCI's gauge of stocks across the globe rose 4.46 points, or 0.45%, to 989.37.

The pan-European STOXX 600 index rose 0.54%.

Earlier, 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, data released on Tuesday showed.

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.

The yield on benchmark U.S. 10-year notes rose 3.4 basis points to 4.37%, from 4.34%.

(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 and Chris Reese)