Boris Johnson has urged David Cameron to do a deal with Vladimir Putin and Bashar al-Assad to defeat Isis in Syria.
However the London mayor's decision to call into question the presence of enough moderate Syrian rebels to help take the fight to Isis was rubbished by Downing Street.
Writing in his Daily Telegraph column on Monday, the mayor of London said despite Putin being "a ruthless and manipulative tyrant" who looks "a bit like Dobby the House Elf", it should not be "morally impossible" to side with Russia against the Islamist extremists.
"This is the time to set aside our Cold War mindset. It is just not true that whatever is good for Putin must automatically be bad for the West. We both have a clear and concrete objective – to remove the threat from Isil. Everything else is secondary," he said.
"We need to focus on what we are trying to achieve. Our aims – at least, our stated aims – are to degrade and ultimately to destroy Isil as a force in Syria and Iraq. That is what it is all about."
Boris also used his column to cast doubt on Cameron's claim there were 70,000 soldiers in the Free Syrian Army (FSA) capable of pushing back Isis.
The presence of the FSA formed a key part of the prime minister's case for expanding RAF airstrikes against Isis from Iraq into Syria.
However Boris said those numbers "may be exaggerated" and suggested many may "not ideologically very different from al-Qaeda".
The mayor said the "obvious" answer was for the West to ally with Syrian president Assad and his army. "Thanks at least partly to Russian air strikes, it looks as if the regime is taking back large parts of Homs. Al-Qaeda-affiliated militants are withdrawing from some districts of the city. Is that a bad thing? I don’t think so," he said.
"The best hope of getting rid of Isil is an agreement between all the powers – America, Russia, France, Britain, Turkey, Saudi Arabia and the rest – to take them out, together with a timetable for Assad to step down and a plan for a new Syrian government."
Asked about Boris' comments, the prime minister's spokesperson said the 70,000 figure was "reached on the basis of evidence of very detailed analysis by diplomats, intelligence experts and others and we are clear that it does not include extremist groups".
Asked why Boris did not agree, the spokesperson replied: "You had better ask Boris Johnson."