The US administration has acted to soothe hurt British feelings by insisting that the special relationship remains intact, after Barack Obama went public with criticism of David Cameron for his actions over Libya.
The American president was critical of European nations - including the UK - which joined the US in military action to prevent a massacre in Libya in 2011, but then failed to prevent the north African country becoming a "mess" in the aftermath of war.
In a lengthy interview in The Atlantic magazine, he put some of the blame for chaos in Libya on Mr Cameron becoming "distracted" by other priorities. And he voiced his frustration with European countries he branded "free riders" for relying on US military muscle to achieve their foreign policy goals.
The magazine reported that Mr Obama privately warned the Prime Minister that, if the UK wanted to maintain the special relationship, it would have to pay its "fair share" on defence by meeting the Nato target of spending 2% of GDP on the military.
However, National Security Council spokesman Edward Price was swift to reassure the UK that "we deeply value the UK's contributions on our shared national security and foreign policy objectives which reflect our special and essential relationship".
Mr Cameron was "as close a partner as the president has had" and had "shown leadership" in meeting the 2% commitment, said Mr Price.
And US ambassador in London Matthew Barzun went on Twitter to insist: "Our relationship is essential. It is special. True yesterday, true today and will be true tomorrow.
"We've long worked together for a more peaceful, prosperous and just world. Look at Nato, Iran deal, counter-terrorism, Ebola, trade and aid."
Mr Cameron's official spokeswoman declined to comment on private conversations between Mr Obama and the Prime Minister, but insisted that Britain had made efforts to help the people of Libya build a stable and peaceful future in the wake of Colonel Muammar Gaddafi's overthrow.
"We would share the president of the United States' assessment that there are some real challenges in Libya," she told a regular Westminster media briefing.
"That is why we are continuing to work hard with our international partners, including the US, and through the United Nations to support the process in Libya that puts in place a government that can bring stability to that country."
In the interview, Mr Obama explained why he had decided to involve the US in military action in Libya, despite some advisers telling him that the situation was not America's problem.
In a remark apparently targeted at the US's European allies, he said there had been "a habit over the last several decades in these circumstances is people pushing us to act but then showing an unwillingness to put any skin in the game ... free riders".
And he added: "What I said at that point was, we should act as part of an international coalition. But because this is not at the core of our interests, we need to get a UN mandate; we need Europeans and Gulf countries to be actively involved in the coalition; we will apply the military capabilities that are unique to us, but we expect others to carry their weight."
Mr Obama said that the intervention "averted large-scale civilian casualties (and) prevented what almost surely would have been a prolonged and bloody civil conflict". But he added: "And despite all that, Libya is a mess."
He added: "When I go back and I ask myself what went wrong, there's room for criticism, because I had more faith in the Europeans, given Libya's proximity, being invested in the follow-up."
Mr Cameron became "distracted by a range of other things", he said. And he said that the then French president Nicolas Sarkozy "wanted to trumpet the flights he was taking in the air campaign, despite the fact that we had wiped out all the air defences and essentially set up the entire infrastructure" for the intervention.
John Baron, the only Conservative MP to vote against British involvement in Libya in 2011, said Mr Obama's criticisms of Europe's handling of the post-conflict situation were correct.
"President Obama is right that Libya is a shambles," said the Basildon and Billericay MP.
"We did not understand the complexities of the situation, or how events would play out post-conflict. This lack of knowledge has once again caused a worse situation, including the presence of extremists such as Daesh, as well as an immigration crisis."
But Andrew Mitchell, who was international development secretary at the time of the Libya intervention, said it was "extremely unfair and completely untrue" to suggest that Mr Cameron had been distracted from Libya by other issues
Mr Mitchell told BBC Radio 4's World At One: "I think (Obama) certainly doesn't appreciate the full extent of the plans that were made for stabilising the situation in Libya when the immediate conflict stopped.
"The problem was, of course, that there was no peace to stabilise. That's why Libya has proved to be so challenging."