Russian President Vladimir Putin has called for a regional "co-ordinating structure" against Islamic State (IS).
Mr Putin reiterated his support for Syrian President Bashar al-Assad, who Western countries and the Syrian opposition have said must go.
The crisis is expected to be high on the agenda as world leaders gather at the UN in New York.
Mr Putin will hold rare talks with US President Barack Obama to discuss the issue later on Monday.
Relations between Russia and the West have been strained over Moscow's annexation of Ukraine's Crimea peninsula last year and support for separatist rebels.
In a separate development, UK Prime Minister David Cameron is expected to soften his stance against Mr Assad in a speech this week.
He is due to tell the annual meeting of the UN General Assembly that Mr Assad could remain temporarily in power at the head of a transitional government.
Mr Cameron — along with Mr Obama and French President Francois Hollande — has previously demanded that Mr Assad be removed from power as a condition of any peace deal, a position consistently rejected by Mr Putin.
Speaking as he arrived in New York on Sunday, Mr Cameron said: "[Bashar al-] Assad can’t be part of Syria’s future. He has butchered his own people. He has helped create this conflict and this migration crisis. He is one of the great recruiting sergeants for Isil [IS]."
Meanwhile, Iranian President Hassan Rouhani — a key regional ally of President Assad — said the government in Damascus "can't be weakened" if IS militants were to be defeated.
He was speaking on the sidelines of the UN General Assembly meeting in New York.
European leaders are intensifying calls for a diplomatic push in Syria in the wake of a massive influx of refugees heading for Europe.
The urgency of finding a diplomatic solution to the conflict has also been reinforced by a Russian military build-up in Syria in support of Mr Assad's regime.
Iraq on Sunday announced that it had signed an agreement on security and intelligence co-operation with Russia, Iran and Syria to help combat IS.
In an interview with CBS television, Mr Putin said the Syrian president's troops were "the only legitimate conventional army there".
He said the troops were fighting terrorist organisations, and Russia "would be pleased to find common ground for joint action against the terrorists".
US Secretary of State John Kerry, however, said the efforts were "not yet co-ordinated" and the US had "concerns about how we are going to go forward".
Analysis: Jeremy Bowen, BBC Middle East Editor
Two factors have put Syria on the priority list for the leaders gathering in New York for the UN General Assembly. One is the threat posed by the jihadists of Islamic State. The other is the refugee emergency, which means that the reverberations of the Syrian war have reached Western Europe.
Now, the military priority is hitting IS.
The British hope that their new stance on President Assad might help to break the deadlock over Syria in the UN Security Council, which has crippled diplomatic attempts to find a way to stop the war.
If the rift in the Security Council over Syria cannot be repaired, Mr Cameron's call for a new diplomatic initiative to end the war won't change anything.
On Sunday, France said it had carried out its first air strikes against IS in Syria, destroying a training camp.
A US-led coalition has been carrying out air strikes against IS in Syria and Iraq for more than a year. France, like the UK, has previously confined its air strikes against the Islamic State group to Iraqi airspace.
The UK announced earlier this month it had carried out a drone strike against two British citizens in Syria but has yet to fly manned operations in Syrian airspace.
More than 200,000 Syrians have been killed since the country erupted into civil war in 2011, and Islamic State took control of swathes of the country in 2014. Mr Assad has been accused of killing tens of thousands of his own citizens with indiscriminate bombing in rebel-held areas.
Approximately four million Syrians have fled abroad so far — the vast majority are in neighbouring Turkey, Lebanon and Jordan — and more are on the move.