Updates prices, market activity, adds commentary; changes byline, dateline, previous LONDON

By Nicole Jao

NEW YORK, March 24 (Reuters) - Oil rallied on Tuesday as the world's biggest supply disruption persisted and Iran denied it held talks with the United States to end the war in the Gulf, contradicting U.S. President Donald Trump, who said a deal could be reached soon.

Crude futures had dropped more than 10% on Monday, after Trump ordered a five-day delay of attacks on Iran's power plants, saying the U.S. had talks with unnamed Iranian officials that produced "major points of agreement".

Brent futures LCOc1 rose $4.19, or 4.19%, to $104.13 a barrel at 12:06 p.m. ET (1606 GMT) on Tuesday. U.S. West Texas Intermediate (WTI) CLc1 climbed $4.24, or 4.81%, to $92.37.

The war has all but halted shipments of about one-fifth of the world's oil and liquefied natural gas through the Strait of Hormuz, causing what the International Energy Agency has called the biggest-ever oil supply disruption.

"The reality on the ground is unchanged," said Nikos Tzabouras, analyst at Jefferies-owned Tradu.com. "The Strait of Hormuz remains effectively closed and supply disruptions linger, tightening the market."

Iran sent waves of missiles into Israel on Tuesday. Three senior Israeli officials, speaking on condition of anonymity, said Trump appeared determined to reach a deal, but that they thought it highly unlikely Iran would agree to U.S. demands in any new round of negotiations.

"We're back climbing the wall of worry," said Phil Flynn, senior analyst with Price Futures Group. "Market is pricing in that the war is going to continue."

Iran's negotiating posture has hardened sharply since the war began, sources told Reuters, adding it would demand significant concessions from the U.S. if mediation efforts lead to serious negotiations.

If the strait remains effectively shut until the end of April, Brent could still reach $150 a barrel, Macquarie said. That would exceed the all-time high of $147 set in 2008.

In the latest attacks on energy infrastructure across the region, a gas company office and a pressure-reduction station were hit in the Iranian city of Isfahan, while a projectile struck a gas pipeline feeding a power station in Khorramshahr, Iran's Fars news agency reported.