Boris Johnson has faced intense criticism for his comments about President Barack Obama's "part Kenyan" ancestry.
The London Mayor said Mr Obama's call for Britain to remain in the EU was "incoherent", "inconsistent", and "downright hypocritical".
Writing in the Sun newspaper, Mr Johnson suggested that the US leader may have an "ancestral dislike of the British empire" because of his heritage.
Shadow chancellor John McDonnell accused Mr Johnson of "dog whistle racism" and called on him to withdraw the comment.
Labour frontbencher Diane Abbott, meanwhile, said Mr Johnson's "offensive" comments echo the right-wing rhetoric espoused by the US "Tea Party".
Mr Johnson said President Obama's administration 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.
"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?"
Sir Stephen Wall, former British permanent representative to the EU, 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."
Labour MP Chuka Umunna also entered the debate, saying Mr Johnson's comments are "beyond the pale".
Mr Johnson's comments were echoed by Ukip leader Nigel Farage, however, who said: "Because of his grandfather and Kenya and colonialisation, I think Obama has a bit of a grudge against this country."