Ronald Reagan issued a last-ditch appeal to Margaret Thatcher to abandon her campaign to retake the Falklands and to hand over the islands to international peacekeepers, according to official documents just made public.
Files released by the National Archives under the 30-year rule show that as British troops closed in on final victory, the US president made a late-night phone call to Thatcher urging her not to completely humiliate the Argentines.
However, his request fell on deaf ears as a defiant prime minister insisted that she had not sent a British task force across the globe just 'to hand over the Queen's islands to a contact group'.
Reagan made his call to Thatcher in Downing Street at 11.30pm London time on May 31, 1982, as British forces were beginning the battle for Port Stanley, the Falklands capital.
The Americans had already proposed sending a joint US-Brazilian peacekeeping mission, and the president suggested that the time had come to show magnanimity.
'The best chance for peace was before complete Argentine humiliation,' he told her.
'As the UK now had the upper hand militarily, it should strike a deal now.'
Thatcher said the United Kingdom could not contemplate a ceasefire without Argentinian withdrawal.
According to the official No 10 note, she told him: 'Britain had not lost precious lives in battle and sent an enormous task force to hand over the Queen's islands to a contact group.
'As Britain had had to go into the islands alone, with no outside help, she could not now let the invader gain from his aggression. The prime minister asked the president to put himself in her position.
'She had lost valuable British ships and invaluable British lives. She was sure that the president would act in the same way if Alaska had been similarly threatened.'
As the battle reached its climax she even drafted a telegram to the Argentinian leader General Leopoldo Galtieri - although it was never sent - demanding for a final time that he withdraw his forces.
'In a few days the British flag will be flying over Port Stanley. In a few days also your eyes and mine will be reading the casualty lists,' she wrote.
'On my side, grief will be tempered by the knowledge that these men died for freedom, justice and the rule of law. And on your side? Only you can answer that question.'
It was not the only time during the conflict that Britain had problems with her closest ally.
On April 21, as the British task force approached the islands, US secretary of state Al Haig told the British ambassador to Washington, Sir Nicholas Henderson, he intended to inform the Argentinian junta that UK troops would be landing on South Georgia, the first of the islands to be seized by the Argentines.
Haig, who had been trying frantically to broker a settlement, insisted that it was the only way he could keep his diplomatic initiative alive.
Henderson told Haig he was going far beyond the obligations of a neutral negotiator and that the information could be used by the Argentines to mount a submarine or suicide air attack on the task force.
Reluctantly, Haig promised to keep quiet.
Overall, however, Henderson concluded that Britain had cause to be grateful to Haig for ensuring a divided Reagan administration ultimately came down on the side of the UK.
It was support that manifested itself in access to the latest US weaponry, vital intelligence, and - most crucially - the use of the American base on Ascension Island, which provided a key staging post for the task force.
'The president did not give a strong lead and allowed the frictions in the decision-making process to continue,' Henderson later noted.
'I am sure, though, that Mr Haig's was the decisive influence throughout: he wanted us to win and would have been horrified if the Argentinians had got away with it.'
The files also include Thatcher's hitherto unpublished testimony to the Franks Inquiry into the conflict.
In it, she described her horror when, at the end of March 1982, she became aware that the Argentinians were about to invade.
'I just say it was the worst, I think, moment of my life,' she told the inquiry.
'I never, never expected the Argentines to invade the Falklands head-on. It was such a stupid thing to do, as events happened, such a stupid thing even to contemplate doing.'
Despite the costs, including the loss of 255 British lives and six ships sunk, Henderson had no doubt that it had been worth it.