Britain, the US and European allies are combining in a drive to persuade Vladimir Putin to co-operate with them in the struggle against terror group Islamic State.
Putin claims the campaign of airstrikes on Syria he launched in September is directed at "terrorists", but the West accuses him of targeting the moderate opposition to president Bashar Assad.
The Prime Minister will seek to reassure Putin that Russia's interests will be "protected" in the transition to a new regime in Damascus. But sources stressed that Britain continues to see no role for Assad - a close ally of Moscow - in a future Syrian administration.
US President Barack Obama is believed to have delivered a similar message to the Russian leader in an unscheduled 35-minute discussion on the fringe of the Antalya summit, which has been dominated by discussions over the world's response to Friday's attacks in Paris and the downing of a Russian airliner in Egypt.
American officials, who characterised the talks as "constructive", said: "President Obama and President Putin agreed on the need for a Syrian-led and Syrian-owned political transition, which would be proceeded by UN-mediated negotiations between the Syrian opposition and regime as well a ceasefire."
Moscow and the West are at loggerheads over Mr Putin's support for Assad. But it is thought that he may be prompted to direct strikes against IS if it is proved that the terror group was responsible for planting a bomb which destroyed the Metrojet Airbus over Sinai at a cost of 224 lives - as Britain believes.
Speaking ahead of Monday's meeting, 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'."
Mr Cameron's talks with Mr Putin will be followed by a meeting of the Quint - an informal group of Western powers within the G20, made up of the UK, US, France, Germany and Italy - to assess progress and discuss how further efforts on Syria can be co-ordinated. And the leaders will observe the international minute's silence for Paris at 11am UK time.
It will be the first time the PM and Russian President have spoken face to face since the Brisbane G20 summit in November 2014, when frosty discussions were dominated by events in Ukraine.
Downing Street sources said Mr Cameron wants to use the talks to explore how Russia and the West can "bridge our differences" over Syria by recognising the shared threat they face from IS and the shared interest they have in finding a way forward.
Mr Cameron will also urge Mr Putin, from a humanitarian point of view, to put pressure on the Assad regime to stop using barrel bombs against its citizens - something which is believed to have driven a recent surge in refugees fleeing the country.
The PM hopes to revive the spirit of lengthy discussions at a 2012 meeting at Putin's dacha in Sochi, when the two men were able to have "deeper" conversations about Syria's future. But sources stressed that the PM was "realistic" about the prospects for swift progress and acknowledged that there was "a lot still to be worked out" before proposals for a settlement for Syria can be agreed.
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.
At a working dinner in Antalya - just 300 miles from the Syrian border - Mr Cameron pushed for a concerted effort to improve airport security around the world.
Pointing out that citizens of G20 states account for 80% of global air travel and their airlines carry 70% of all the world's passengers, the Prime Minister urged them to develop robust and consistent global aviation security standards.
And he said they should help poorer states financially to enable them to raise their standards, and to assist those - like Tunisia - whose tourist industries have suffered a slump in business as a result of terrorism.