Russian president Vladimir Putin said on Monday that he would back parts of the Syrian opposition with air support in a joint fight against Islamic State in northern Syria, in the first concrete sign that Russia and the west can set aside their differences over the political future of President Bashar al-Assad in order to defeat Isis.

Hinting at the Russian change of policy, David Cameron said there were “some signs” during talks with Putin on the margins of the G20 summit that Russia would no longer focus bombing raids on moderate Syrian forces.

Putin’s offer, if it turns into reality, is potentially the biggest military breakthrough in Syria for some months, and allied with the pressure being applied to Isis in Iraq, could start to change the military equation in Syria.

The quest for an end to the four-year civil war in Syria – which has prompted a mass migration and terror crisis in Europe – has been stymied by the Russian and Iranian refusal to abandon Assad.

Since September, Putin has stepped up his support for Assad by bombing anti-Assad forces – including the more moderate opposition groups supported by the west.

Speaking at the close of the G20 summit in Antalya in southern Turkey, Putin said: “A part of the Syrian opposition considers it possible to begin military actions against Isil [Isis] with the assistance of the Russian air forces, and we are ready to provide that assistance.”

If this happens, Assad’s army and the opposition will fight a common enemy, he outlined.

“It’s not the time to debate who is more effective in the fight against Isil, what we need to do is consolidate our efforts,” added Putin.

The formal agenda of the two-day G20 summit rapidly became swamped by the issue of how the world leaders should respond to the murder of at least 129 people in Paris on Friday, for which Isis has claimed responsibility.

Both Cameron and Barack Obama met Putin to urge him to shift his focus to an attack on Isis, as well as to agree a political process that might lead to the removal of Assad in 18 months, after elections.

Cameron hinted at possible flexibility in Putin’s position, saying: “We think bombing the Syrian Free Army – that can play a part and should play a part in the future of Syria – is a mistake. I made that view absolutely clear to President Putin; there are some signs, some signs, that they are focusing on Isil and we need to see if that continues.

“Everyone recognises there is a need for compromise. The gap has been enormous between those, like us, who say President Assad must go immediately and those who continue to support him.

“It is not as if there has been a British pride or stubbornness, an American stubbornness or a Saudi stubbornness. This is for the Syrian people. If you barrel-bomb your own nation and rain down destruction on your own people, it’s obvious that they won’t accept him as their leader.

“That is the gap we have and it has been reduced. I hope we can close the gap still further but it will need compromise on both sides.

“I have said Assad should go immediately and we have come to recognise there is a transition. We have never argued that the right answer is take away all the elements of the Syrian state.”

Cameron added: “Some elements of the state need to continue. We need to find elements in the government – Christians, Kurds and Alawites – so that government represents all of Syria and that is the process that needs to be gone through.”

Under political and media pressure to come up with a new, faster strategy to defeat Isis in the wake of the Paris attacks, Obama again insisted the current strategy was ultimately going to work, but will be intensified.

He said the key was reduce the size of territory over which Isis holds sway, and to intensify intelligence co-operation with the French.

He said he had ruled out the idea of putting as many as 50,000 troops on the ground or setting up safe havens. He said: “That would be a mistake, not because our military could not march into Mosul or Raqqa or Ramadi and temporarily clear out Isil, but because we would see a repetition of what we’ve seen before, which is if you do not have local populations that are committed to inclusive governance and who are pushing back against ideological extremes, that they resurface unless we’re prepared to have a permanent occupation of these countries.

“One of the challenges we have in this situation is that if you have a handful of people who don’t mind dying, they can kill a lot of people. That’s one of the challenges of terrorism. It’s not their sophistication or the particular weaponry that they possess, but it is the ideology they carry with them and their willingness to die.”