Barack Obama warned David Cameron that Britain would have to pay "your fair share" on defence if it was to maintain its special relationship with the US, it has been reported.
Details of the US president's warning came in a lengthy interview in The Atlantic magazine, in which Mr Obama explained his frustration with "free riders" in the international community who call for action in humanitarian and security crises but fail to make their own military resources available.
Mr Obama 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.
The US president said that Mr Cameron became "distracted" from Libya by other priorities, while he accused then French president Nicolas Sarkozy of seeking to hog the spotlight for his part in countering dictator Muammar Gaddafi's attempt to put down a rebellion.
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 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."
The President is understood to have pressed Mr Cameron to meet Nato's target of spending 2% of GDP on defence at last June's G7 summit in Germany.
The Prime Minister was coming under pressure from Conservative backbenchers not to allow spending on the military to fall below the Nato benchmark, and shortly afterwards committed himself to hitting the 2% figure.
The Atlantic reported that Mr Obama told Mr Cameron the UK would no longer be able to claim a "special relationship" with the United States if it did not commit to the 2% figure, saying: "You have to pay your fair share."
"Free riders aggravate me," the President told the magazine.
And he 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.
"The way I looked at it was that it would be our problem if, in fact, complete chaos and civil war broke out in Libya," said Mr Obama. "But this is not so at the core of US interests that it makes sense for us to unilaterally strike against the Gaddafi regime.
"At that point, you've got Europe and a number of Gulf countries who despise Gaddafi, or are concerned on a humanitarian basis, who are calling for action. But what has 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.
"So 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 left no doubt that he felt blame rested with Europe over the continuing chaos in Libya.
"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," said Mr Obama.
Mr Cameron became "distracted by a range of other things", he said. And he said that Mr 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.
The PM's spokeswoman said that Mr Cameron had made clear many times that he still believes military intervention in Libya was "absolutely the right thing to do" and noted that he had put support for the country on the agenda when the UK hosted the G8 in Northern Ireland in 2013.