On a visit to the UK, Obama weighed in to Britain's debate about European Union membership, urging voters to back staying in the 28-nation bloc.
At a news conference with Prime Minister David Cameron, Obama said "I don't think the EU moderates UK influence in the world it magnifies it."
His opinion also expressed in a Daily Telegraph newspaper article angered campaigners for a "leave" vote in the June 23 referendum, who accused the president of meddling.
Writing in The Sun newspaper, Johnson recounted a claim that a bust of former British Prime Minister Winston Churchill was removed from the Oval Office after Obama was elected and returned to the British Embassy.
Johnson wrote that some said removing the bust "was a symbol of the part-Kenyan president's ancestral dislike of the British Empire, of which Churchill had been such a fervent defender."
Obama's late father was from Kenya, a former British colony that gained independence in the 1960s.
But the mayor's comments drew criticism from his political opponents. Former Liberal Democrat leader Menzies Campbell said "this attack constitutes an unacceptable smear."
"Many people will find Boris Johnson's loaded attack on President Obama's sincerity deeply offensive," he said.
Stephen Wall, former British permanent representative to the European Union, said: Johnson's comment about the president's Kenyan heritage "is demeaning to the debate," and Labour Party lawmaker Diane Abbott said that "Boris dismissing president Obama as 'half-Kenyan' reflects the worst Tea Party rhetoric."
