David Cameron is to urge Vladimir Putin to focus Russia's firepower on destroying the terror group Islamic State.
The Prime Minister will use a meeting with Mr Putin at the G20 summit in Turkey on Monday to voice the West's concern that Russian airstrikes are targeting moderate opponents of Syrian President Bashar Assad, rather than the terror group which has claimed responsibility for the slaughter on the streets of Paris.
Speaking shortly after leaders of the world's major economies bowed their heads for a minute's silence in honour of victims of terror in Paris and the Turkish capital Ankara, Mr Cameron said that Britain and the rest of the world would be safer if IS - also known as Isil, Isis and Daesh - was destroyed "once and for all".
The Prime Minister said that the murders in Paris made it even clearer that the fight against the terror group must take place both in Iraq and Syria.
He has long argued that RAF missions against IS in Iraq should be extended to Syria, where the US and France are already conducting strikes.
But Mr Cameron has held back from calling a House of Commons vote because he is not sure of achieving a consensus.
Speaking at the G20 summit venue in Antalya - just 300 miles from the Syrian border - Mr Cameron said: "It's become even more clear that our safety and security depends on degrading and ultimately destroying Isil whether it's in Iraq or Syria.
"We're playing a huge role in that already in Iraq. Others are taking action in Syria which we both support and enable, but we've got to keep on making the case that we will be safer in the UK, in France, right across Europe if we destroy this death cult once and for all.
"We have our differences with the Russians, not least because they've done so much to degrade the non-Isil opposition to Assad, people who could be part of the future of Syria.
"But the conversation I want to have with Vladimir Putin is to say `Look, there is one thing we agree about which is we'd be safer in Russia, we'd be safer in Britain if we destroy Isil. That's what we should be focusing on'."
French President Francois Hollande was absent from the annual G20 gathering, staying home to lead his country's response to the slaughter in Paris.
Mr Cameron joined fellow leaders including US President Barack Obama and Russian President Vladimir Putin in bowing their heads for a moment to remember the victims of Friday's gun and bomb attacks, as well as the 102 killed by two blasts at a demonstration in the Turkish capital on October 10.
After meeting the summit's host, Turkish President Recep Tayyip Erdogan, Mr Obama vowed that the US would "redouble efforts" to prevent further attacks by Islamic State, which has claimed responsibility for the Paris atrocities, has been blamed for the Ankara massacre, and is believed by Britain to be guilty of downing a Russian airliner over the Sinai peninsula in Egypt last month.
"Traditionally the G20 has been a forum primarily to discuss economic issues facing the globe," said the US president. "(But) the sky has been darkened by the horrific attacks that took place in Paris just a day and a half ago.
"The United States and its allies will redouble efforts to find a peaceful solution in Syria and prevent Islamic State militants from perpetrating attacks like those in Paris."
Mr Obama held talks lasting 35 minutes with Mr Putin, which the US characterised as "constructive".
The fight against terror has overshadowed the economic issues on the official agenda for the summit. And issues like migration and the search for peace in Syria are being seen through the prism of the violence in Paris.
Following the discovery near the body of one of the killers of a passport belonging to a Syrian refugee who entered the EU through Greece, questions were being raised about the future of the border-free travel arrangements in place in much of continental Europe.
European Commission president Jean-Claude Juncker urged member states not to ditch the EU's refugee policy, saying: "We should not mix the different categories of people coming to Europe. The one responsible for the attacks in Paris ... he is a criminal and not a refugee and not an asylum seeker.
"I would invite those in Europe who try to change the migration agenda we have adopted - I would like to remind them to be serious about this and not to give in to these basic reactions that I do not like. I see the difficulty but I don't see the need to change our general approach."
Moscow and the West are at loggerheads over Mr Putin's support for Assad. A meeting of foreign ministers in Vienna on Saturday agreed a two-year timeline towards the election of a new government in Damascus, but key details remained unresolved, including what part Assad might play in any new settlement and a decision on which opposition groups should be shunned as terrorists. Only IS and al Qaida affiliates were specifically excluded from arrangements for proposed ceasefires.
With the attention of the West increasingly focused on the elimination of the threat from IS, Mr Putin can be expected to urge the Prime Minister on Monday to give up Britain's insistence that Assad can have no long-term role in a future administration.
Washington is known to be concerned that US jets conducting strikes against IS strongholds in Syria do not come into conflict with Russian planes - a danger which is also believed to be a factor in Mr Cameron's decision not to press ahead so far with a Commons vote on extending RAF missions into Syria.
European Council president Donald Tusk called for a united front against IS. "It should be our common aim to co-ordinate our actions against Daesh, and for sure the co-operation between the United States and Russia is a crucial one," he said.
Mr Erdogan has said that concerted action in the fight against terrorism should be "put at the forefront".
Turkey, which has a 500-mile border with Syria, has granted the US-led coalition access to its air bases to launch strikes against IS. Turkish media reported that four IS militants were killed after opening fire on soldiers in the east of the country on Saturday.