Obama and Cameron 'close partners', White House insists
The White House says David Cameron has been "as close a partner" as Barack Obama has had, after the president appeared to criticise the PM.
Mr Cameron had become "distracted" after the 2011 intervention in Libya, Mr Obama told the Atlantic magazine. He also described Libya as "a mess".
But in an email to the BBC, a White House spokesman said the US "deeply" valued the UK's contributions.
No 10 said the UK-US relationship remained "special and essential".
In the article Mr Obama reflected on "what went wrong" after the overthrowing of the Gaddafi regime, led by the UK and France.
"There's room for criticism, because I had more faith in the Europeans, given Libya's proximity, being invested in the follow-up," he said.
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Mr Obama said the UK prime minister soon became "distracted by a range of other things".
The US president said of the North African country: "We averted large-scale civilian casualties, we prevented what almost surely would have been a prolonged and bloody civil conflict. And despite all that, Libya is a mess."
He also spoke of "free riders", saying European and Gulf countries were calling for action against Gaddafi - but, he said, the "habit" for several decades had been "people pushing us to act but then showing an unwillingness to put any skin in the game".
In its email to the BBC later, the White House said: "Prime Minister Cameron has been as close a partner as the president has had, and we deeply value the UK's contributions on our shared national security and foreign policy objectives which reflect our special and essential relationship."
On Libya, it said the president had always said "all of us... could have done more".
The White House also said the UK had "stepped up on a range of issues", including a pledge to spend 2% of national income on defence.
According to the article, this pledge came after Mr Obama told Mr Cameron that Britain must pay its "fair share" if it wanted to continue to claim a "special relationship" with the US.
The prime minister's official spokeswoman said the relationship between the UK and US "remains a special and essential relationship, as both sides of the Atlantic have said and reiterated in the last day".
She said there was "regular dialogue" between the two leaders' offices on "a whole range of issues".
Responding to suggestions Mr Cameron had been angered by Mr Obama's comments, she said Libya had been "an extremely challenging situation".
She added: "We have done all we can. We think it has been the right approach to try and support a Libyan-led process and that is why we will continue to pursue that type of approach."
US ambassador in London Matthew Barzun told the BBC the relationship between the US and UK "is special and is essential".
He added: "The engagements between our countries' leaders are frequent and they publicly stand up together and talk about what's important. They privately talk all the time and I think that's really important and I wouldn't put over focus on one interview and one paper."
By BBC political correspondent Iain Watson
The "special relationship"- always more special to the UK than the US - has survived bigger strains: Suez, Vietnam; the Falklands; and the US invasion of Grenada, to name but a few.
So some disparaging remarks about a British prime minister from an American president doesn't really rate as earth-shattering.
Nonetheless, there is little doubt that No 10 were irritated.
At a press briefing yesterday his spokeswoman said the prime minister couldn't really let a leader - Colonel Gaddafi - torture and terrorise his own people.
The problem is that the president is now looking back on his two terms in the White House, while the PM is fighting for his future in an EU referendum.
So the US moved swiftly to patch up the rocky relationship, sending around the equivalent of flowers after a lovers' tiff in the form of fulsome praise for David Cameron.
But that came too late to avoid the collateral damage delivered to his reputation from the president's candid comments.
Former Conservative foreign secretary Sir Malcolm Rifkind said criticism for the UK was "pretty rich" because the Americans "did far less" than France or the UK in the aftermath of the intervention.
Oliver Miles, former British ambassador to Libya, said he believed Mr Obama's comments about Mr Cameron being distracted had been "inaccurate" but were not a "big deal".
Andrew Mitchell, who was International Development Secretary during the invasion of Libya, said the President's comments were "extremely unfair and completely untrue".
"It was always clear that there wouldn't be boots on the ground. The House of Commons would never have agreed to British boots on the ground in Libya."
January 2011: A wave of uprisings sweeps the Arab world, eventually reaching Libya
February 2011: Anti-Gaddafi protests erupt on the streets of the second-largest city, Benghazi, spreading to other cities
March 2011: The UN Security Council authorises a no-fly zone over Libya and air strikes to protect civilians. UK MPs vote to authorise military action
August 2011: Rebel fighters enter Tripoli. Col Gaddafi goes into hiding
October 2011: Gaddafi is captured and killed by rebel fighters in the city of Sirte
The 2011 armed rebellion assisted by Western military intervention led to the end of Muammar Gaddafi's 42-year dictatorship. But it left a power vacuum and instability, with no authority in full control.
Despite efforts to support Libya's National Transitional Council, and the first elections in the country for decades, it rapidly descended into violence, with two rival militia-backed parliaments.
A recent UN report said there were hundreds of armed groups and the chaos has allowed so-called Islamic State to gain a foothold.