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Asked about the prospect of Mr Johnson standing for a third term as mayor, a No 10 spokesman said:
"The Prime Minister thinks Boris Johnson is doing an excellent job as mayor of London and long may he continue to do so."
Boris Johnson could still reverse his decision not to seek a third term as London mayor, he indicated today - but only if there was strong public support for him to continue.
The senior Tory - widely tipped as a successor to David Cameron as party leader - joked that he could be persuaded to stand again if there was a "Reverse Morsi" in the capital.
His quip about the mass protests taking place in Cairo against the Egyptian president came as he faced questions about his ambition to be prime minister during the first edition of his new monthly radio phone-in.
Mr Johnson has declared that he will step down when his second four-year term at City Hall ends in 2016 but has since conceded that he regretted that decision.
Asked about his future plans he said politicians should be careful not to "do things for too long" but admitted that he had discussed the idea of staying in with friends.
"You mean, if it was a sort of a 'reverse Morsi' situation? If there were hundreds of thousands of people actively calling for an extension of the administration?" he asked.
"The truth is that there are so many things we are trying to do at the moment that I know I am not going to be able to get in in time for 2016 that it is becoming increasingly...
"I won't deny it, it is something I think about and something that I've even talked to friends about.
"But the reality is that after eight years you've been at it for a long time in a very big job. You see what happens to people who do things for too long. You've got to be fair to the electorate, you've got to be sure you are doing your best.
"There will come people who will have fantastic ideas and who will have fresh ways of thinking about things."
Labour predecessor Ken Livingstone achieved some good things for London but "wanted to go on for too long", he said.
"The truth is, I'm stepping down in 2016. After that, who knows what will happen."
But pressed again if he was sure he could not be persuaded to stay, he added: "It would have to be pretty massive. You really would have to get Trafalgar Square full."