Adds Trump quotes and details, paragraphs 11-16

By Steve Holland and Matt Spetalnick

WASHINGTON, April 7 (Reuters) - President Donald Trump said on Monday that the United States and Iran were beginning direct talks on Tehran's nuclear program, a surprise announcement after Iranian officials had appeared to rebuff U.S. calls for such negotiations.

Iran had pushed back against Trump's demands that it directly negotiate over its nuclear program or be bombed, though it had initially left the door open to indirect discussions.

"We're having direct talks with Iran, and they've started. It'll go on Saturday. We have a very big meeting, and we'll see what can happen," Trump told reporters in the Oval Office during talks with visiting Israeli Prime Minister Benjamin Netanyahu.

"And I think everybody agrees that doing a deal would be preferable," Trump said. He declined to say where the talks would take place.

Warnings by Trump of military action against Iran had jangled already tense nerves across the Middle East after open warfare in Gaza and Lebanon, military strikes on Yemen, a change of leadership in Syria and Israeli-Iranian exchanges of fire.

Trump has said he would prefer a deal over Iran's nuclear program to a military confrontation and he said on March 7 he had written to Supreme Leader Ayatollah Ali Khamenei to suggest talks. Iranian officials said at the time that Tehran would not be bullied into negotiations.

During his 2017-2021 term, Trump withdrew the U.S. from a 2015 deal between Iran and world powers designed to curb Iran's sensitive nuclear work in exchange for sanctions relief. Trump also reimposed sweeping U.S. sanctions.

Since then, Iran has far surpassed that deal's limits on uranium enrichment.

Western powers accuse Iran of having a clandestine agenda to develop nuclear weapons capability by enriching uranium to a high level of fissile purity, above what they say is justifiable for a civilian atomic energy program.

Tehran says its nuclear program is wholly for civilian energy purposes.

Like U.S. presidents before him, Trump has said that Iran cannot be allowed to develop a nuclear weapon.

He told reporters that Saturday's talks with Iran would be at a very high level and he held out the possibility that a deal could be reached. "We have a very big meeting on Saturday and we're dealing with them directly," Trump said.

The White House National Security Council did not immediately respond to a request for details.

The shift comes at a precarious time for Tehran's regional "Axis of Resistance" which it has established at great cost over decades to oppose Israel and U.S. influence. The axis has been severely weakened since Palestinian group Hamas' attack on Israel on October 7, 2023, tipped the Middle East into conflict.

Hamas in Gaza and Hezbollah in Lebanon have been hammered by Israel since the Gaza war began while the Houthi movement in Yemen has been targeted by U.S. airstrikes since last month. Israel severely damaged Iran's air defenses last year.

The fall of Syrian President Bashar al-Assad, another key Iranian ally, has further weakened the Islamic Republic's influence.

(Reporting By Jarrett Renshaw and Matt Spetlanick; Editing by Howard Goller)

((jarrett.renshaw@thomsonreuters.com; (646) 223-6193;))