Boris Johnson has come under fire over his attack on the "part-Kenyan" president Barack Obama.
The Brexit-backing London mayor said it was "incoherent", "inconsistent" and "downright hypocritical" for the US leader to intervene in the European Union referendum row.
But critics accused him of making a "loaded" attack by referring to the president's ancestry, with Labour frontbencher Diane Abbott claiming Mr Johnson's "offensive" comments echoed those of the "Tea Party" right-wing tendency in the US.
And Downing Street said Mr Johnson was recycling "false" claims about the removal of a bust of Winston Churchill from the Oval Office when Mr Obama became president.
In an article for The Sun, the mayor said that "no-one was sure whether the president had himself been involved in the decision" to remove the bust.
"Some said it was a snub to Britain," he said. "Some said it was a symbol of the part-Kenyan president's ancestral dislike of the British empire - of which Churchill had been such a fervent defender."
The mayor continued by arguing that Mr Obama and the US would never agree to the kind of arrangements the UK has as a member of the EU.
"It is deeply anti-democratic - and much as I admire the United States, and much as I respect the president, I believe he must admit that his country would not dream of embroiling itself in anything of the kind," he said.
"It is incoherent. It is inconsistent, and yes, it is downright hypocritical. The Americans would never contemplate anything like the EU, for themselves or for their neighbours in their own hemisphere. Why should they think it right for us?"
Former Liberal Democrat leader Lord Campbell of Pittenweem said Mr Johnson's comments were "an unacceptable smear".
He said: "Many people will find Boris Johnson's loaded attack on president Obama's sincerity deeply offensive. If this is an illustration of the kind of diplomacy that we might expect from a Johnson leadership of the Tory Party then heaven help us.
"In truth this attack constitutes an unacceptable smear."
Shadow international development secretary Ms Abbott said: "Boris dismissing president Obama as 'half-Kenyan' reflects the worst Tea Party rhetoric".
Asked how David Cameron viewed Mr Johnson's comments on the president's "half-Kenyan" heritage, the Prime Minister's official spokeswoman said: "It is important to engage with the facts.
"If you look at the issue the mayor of London was talking about, which related to the bust of Churchill in the Oval Office, they have been clear that this suggestion that he asked for it to be moved and that it is a failure of the president's appreciation of the special relationship is false.
"That decision had already been taken before president Obama took office, so let's focus on the facts."
Sir Stephen Wall, former British permanent representative to the European Union, said: "Boris Johnson's comment implying the President of the United States is driven by his ancestral dislike of the British Empire is demeaning to the debate. Using that type of language does not reflect Britain's standing in the world or the country we aspire to be.
"As our most important ally, President Obama has the right to offer his view and he has made it clear that being in Europe magnifies British influence and enhances Britain's global leadership."
And former UK ambassador to Washington Lord Kerr said: "The US has an interest in Britain, its closest ally, being stronger, safer and better off in the EU - not weaker, out on its own. To claim that the American president has no right to say what he believes, and speak up for US political, economic and business interests is typical Boris bluff and bluster."
Labour MP Chuka Umunna said Mr Johnson's comments were "beyond the pale".
"Once again we see the ugly face of the Tory Party. The nasty party is back," said Mr Umunna.
"Zac Goldsmith has played on Sadiq Khan's Muslim heritage to try to link him with radical extremists, and today Boris Johnson has played on Barack Obama's Kenyan ancestry to question his motives around the EU referendum debate.
"This is beyond the pale and base politics of the worst kind. We may have come to expect this from Donald Trump - but Goldsmith and Boris should know better, and Londoners deserve better."
And Tory MP Nicholas Soames - the grandson of Sir Winston Churchill - said Mr Johnson was being "even more unreliable and idle about the facts than usual".
"There remains a WSC (Winston Spencer Churchill) bust in White House in President's apartments," said Sir Nicholas on Twitter.
But Ukip leader Nigel Farage echoed the Mayor's comments: "His first day in the White House, he had the bust of Winston Churchill removed from the Oval Office.
"Because of his grandfather and Kenya and colonialisation, I think Obama has a bit of a grudge against this country."