Just after midnight in Tehran this week, a motorcade racing to the airport screeched to a halt. Qatari officials jumped out and huddled on the side of the road. Another last-minute crisis had hit the marathon Iran talks, and the Qataris had clear orders: don't leave without an announced deal.

In Washington, Donald Trump was getting ready for a birthday dinner. International mediators believed the birthday — and a UFC cage match scheduled for Sunday night — could put the US president in the mood to sign. In Israel, officials were already grappling with what looked like their closest ally making a separate peace with their archenemy.

Back on that Tehran roadside, the Qataris sorted out the wording disputes. They got back in their cars and headed for the airport. Pakistani Prime Minister Shehbaz Sharif announced the deal at 12:45 a.m. Monday in Tehran. Trump confirmed it minutes later, revealing a goodwill gesture: the US would lift its naval blockade of Iranian ports immediately.

Last weekend, four months of war and 47 years of confrontation between the US and Iran came to a head in an extraordinary diplomatic rush that repeatedly threatened to spiral into more bloodshed. Negotiators were wrangling over issues with huge significance for the world economy, Middle East geopolitics, and US domestic politics.

Trump wanted a deal he could sell as making good on his promise to stop Iran getting a nuclear weapon — even though specific protections were kicked to later talks. Iran was determined to keep what it calls its right to enrich uranium, while squeezing as much as it could in exchange for reopening the Strait of Hormuz.

This account of the final hours comes from interviews with officials in Washington, Europe, and across the Middle East, most speaking anonymously about the secret talks.

Already, Trump is facing criticism — even from some supporters — that the "memorandum of understanding" gives away too much. The text, released by the White House on Wednesday, would reopen the Strait of Hormuz and outlines a $300 billion ($425 billion AUD) plan for Iran's reconstruction and development. But it pushes nuclear talks into future negotiations, essentially punting on the hardest issue.

Throughout the weekend, Iran kept pushing for more US concessions despite the constant threat of more airstrikes — which Trump renewed on Wednesday. Israeli officials fretted they weren't convincing the US that the deal could create grave risks to Israel's security and leave the nuclear issue unaddressed. Qatari mediators told the Iranians they needed to give final sign-off before the start of the UFC match on the White House lawn.

Trump appeared eager to get the deal done. That wasn't lost on another key mediator, Pakistan. Two experts familiar with Pakistan's mediation said army chief Syed Asim Munir wanted the deal signed on Trump's birthday. "The birthday was a way to woo him," said Qamar Cheema, head of an Islamabad-based research institute privy to Pakistan's role. Another person familiar insisted the birthday had nothing to do with the timing.

But two Iranian officials said Tehran waited until midnight local time to finalise — because it didn't want the momentous occasion to coincide with Trump's birthday. The 7½-hour time difference let both sides claim their preferred version of when the deal was finalised. Trump said it would be Sunday; Iran said it would be a later day.

Since announcing a ceasefire with Iran in April, Trump had repeatedly cycled between claiming a peace deal was near, threatening devastating bombardment, and backing away. Last week looked like another such episode: escalation began with the downing of an American helicopter and ended last Thursday with Trump calling off a planned attack. A drawn-out period of stalled talks and simmering violence seemed likely.

US intelligence officials were deeply sceptical of Iran's willingness to make meaningful concessions. The deal now faces a tough road ahead, with critics on both sides and the hardest issues — nuclear enrichment — still unresolved.

"The birthday was a way to woo him"

— Qamar Cheema, head of an Islamabad-based research institute