(Adds Pompeo meeting Saudi king, crown prince; Hook comments)

* Iran brushes off U.S. cyber attacks

* Britain fears "accidental war"

* Iran, U.S. say other side must move first before talks

By Stephen Kalin and Bozorgmehr Sharafedin

JEDDAH, Saudi Arabia/LONDON, June 24 (Reuters) - Iran said on Monday U.S. cyber attacks on its military had failed, while also hinting that it could be willing to discuss new concessions with Washington if the United States were to lift sanctions and offer new incentives.

The longtime foes have come the closest in years to a direct military confrontation in the past week with the shooting down of a U.S. drone by Iran. U.S. President Donald Trump aborted a retaliatory strike just minutes before impact.

U.S. media have reported that the United States launched cyber attacks even as Trump called off the air strike. The Washington Post said on Saturday that the cyber strikes, which had been planned previously, had disabled Iranian rocket launch systems. U.S. officials have declined to comment.

"They try hard, but have not carried out a successful attack," Mohammad Javad Azari Jahromi, Iran's minister for information and communications technology, said on Twitter.

"Media asked if the claimed cyber attacks against Iran are true," he said. "Last year we neutralised 33 million attacks with the (national) firewall."

Allies of the United States have been calling for steps to defuse the crisis, saying they fear a small mistake on either side could trigger war.

"We are very concerned. We don't think either side wants a war, but we are very concerned that we could get into an accidental war and we are doing everything we can to ratchet things down," British Foreign Secretary Jeremy Hunt said.

U.S. Secretary of State Mike Pompeo jetted to the Middle East to discuss Iran with the leaders of Saudi Arabia and the United Arab Emirates, two Gulf Arab allies that favour a hard line. Pompeo met King Salman as well as the king's son, de facto ruler Crown Prince Mohammed bin Salman.

The U.S. special representative for Iran, Brian Hook, visited Oman and was headed to Europe to explain U.S. policy to allies. He told European reporters on a phone call ahead of his arrival that Trump was willing to sit down with Iran, but Iran must do a deal before sanctions could be lifted.

CONCESSIONS

U.S.-Iran relations began to deteriorate last year when the United States abandoned a 2015 agreement between Iran and world powers designed to curb Iran's nuclear programme in return for the lifting of sanctions.

They got sharply worse last month when Trump tightened sanctions, ordering all countries to stop buying Iranian oil.

Recent weeks saw a military dimension to the confrontation, with the United States blaming Iran for attacks on vessels at sea, which Iran denies. Iran shot down the drone, saying it was in its air space, which Washington disputes. Washington also blames Iran for attacks by its Yemeni allies on Saudi targets.

Washington argues that the 2015 nuclear agreement known as the JCPOA, negotiated under Trump's predecessor Barack Obama, did not go far enough, and that new sanctions are needed to force Iran back to the table to make more concessions.

Throughout the escalation, both sides have suggested they are willing to hold talks but the other side must move first. In the latest comment from Tehran, an adviser to President Hassan Rouhani repeated a longstanding demand that Washington lift sanctions in line with the deal.

But the adviser, Hesameddin Ashena, also tweeted a rare suggestion that Iran could be willing to discuss new concessions, if Washington were willing to put new incentives on the table that go beyond those in the deal.

"If they want something beyond the JCPOA, they should offer something beyond the JCPOA; with international guarantees."

Iran's foreign ministry spokesman, Abbas Mousavi, was quoted by ISNA news agency as saying on Monday Tehran did not "want a rise of tensions and its consequences".

U.S. allies in Europe and Asia view Trump's decision to abandon the nuclear deal as a mistake that strengthens hardliners in Iran and weakens the pragmatic faction of Rouhani.

Trump has suggested that he backed off the military strike against Iran in part because he was not sure the country's top leadership had intended to shoot down the drone. However, an Iranian commander said Tehran was prepared to do it again.

"Everyone saw the downing of the unmanned drone," navy commander Rear Admiral Hossein Khanzadi was quoted on Sunday as saying by the Tasnim news agency. "I can assure you that this firm response can be repeated, and the enemy knows it." (Reporting by Bozorgmehr Sharafedin in London and Stephen Kalin in Jeddah Additional reporting by Robin Emmott in Brussels Writing by Peter Graff Editing by Jon Boyle)

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