The mayor of London, Boris Johnson, risked creating a rift with David Cameron yesterday when he said he would be honoured to lead the country.

Speaking in Beijing, where he will play a key role in the closing ceremony of the Olympic Games today, Johnson refused to rule out running for prime minister in the future. He said it would be an “absolute privilege” to take on the top job if others believed he should do it.

Although he emphasised that the scenario was “highly unlikely”, Johnson made it clear that he will serve a maximum of two terms as mayor if he is reelected – potentially leaving him free to challenge Cameron for the Tory leadership some time after the London Olympics in 2012.

Johnson’s remarks threaten to create a crack in his relationship with Cameron, fuelling speculation at Westminster that he has secretly set his sights on the Tory leader’s job.

As the capital’s mayor, in charge of a £12 billion budget, he is the most powerful Conservative in the country. But he has irritated Tory headquarters by rubbishing one of Cameron’s favourite soundbites about Britain’s “broken society”.

Asked about whether he was interested in reaching No 10, he said: “I do think it is highly unlikely that I would be called upon to serve in that office . . . Were I to be pulled like Cincinnatus from my plough, then obviously, you know, it would be an absolute privilege to serve.”

Cincinnatus was a hero of the Roman republic who returned to his farm after serving as consul, but was persuaded to come back as dictator to save the state in a military crisis.

Johnson’s circle privately admit that he has been able to use his role at the Olympics to bolster his long-term ambitions. They concede that the mayor, who flew to China ostensibly to promote London 2012, has boosted his international profile substantially on the trip. While Cameron will have to watch the handover of the Olympic flag at home, Johnson will be treated as an international statesman in the bird’s nest stadium.

During the Games he has been seated alongside Gordon Brown and shared a drink and a chat with Sarah, the prime minister’s wife, on Friday. He has meetings with ministers scheduled when he returns.

Yesterday he shrugged off the controversy he had caused by describing as “piffle” Cameron’s claim that Britain is a broken society. Johnson said that although Britain had problems such as youth crime, they were like a broken fridge that could be repaired rather than a washing machine that did not function at all.

Yesterday he emphasised that there could be a “long wait” before anyone pressed him to run for prime minister. However, one of his closest allies said: “There is no doubt he believes he could do it. He is a superb tactician. Boris is aware that the Conservatives have been out of the limelight for too many years on the global stage and this will mean people around the world seeing him as the No 1 Tory in Britain.

“This has been an opportune shop window for Boris to put on display his superb political skills and he has seized it with both hands.”

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