The White House says David Cameron has been “as close a partner” as Barack Obama has had, after the president appeared the 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.
Downing Street said Britain was still “working hard” in Libya.
BBC North America editor Jon Sopel said the unsolicited statement put out by the White House suggested Downing Street had reacted angrily to the article in the Atlantic.
“It’s like we’ve seen a curtain drawn back on the unspun thoughts of President Obama, complete with frustration as well, and what we’ve seen… is the White House trying to close the curtain as quickly as it can,” he added.
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In its statement, 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.
“With respect to Libya, the president has long said that all of us – including the United States – could have done more in the aftermath of the Libyan intervention.”
It 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 Atlantic’s 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 toppling of the Gaddafi regime in Libya led to a power vacuum and instability, with no authority in full control.
The intervention was led by the UK and France – and in his interview, Mr Obama reflected on “what went wrong”, saying: “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 Mr Cameron became “distracted by a range of other things”.
He also criticised Nicolas Sarkozy, saying the former French president “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.
Mr Obama 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 statement, Downing Street highlighted the White House’s positive comments about the relationship between Mr Cameron and Mr Obama.
It added: “We agree that there are still many difficult challenges in Libya but, as the PM has said many times before, coming to the aid of innocent civilians who were being tortured and killed by their leader was the right thing to do.”
It said the UK had “sought to support the people of Libya” and was still “working hard to support the UN-led process to establish a stable and inclusive government”.
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 governments and the formation of hundreds of militias, some allied to so-called Islamic State.
In January, Mr Cameron told MPs the Libyan people “were given the opportunity” to build a stable democracy – and it was a matter of “huge regret” they had not taken it.