Boris Johnson has come under fire over his attack on the "part-Kenyan" US 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 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 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 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."