The Russians are a key ally of Syrian President Bashar al-Assad.
Western leaders have recently softened their stance towards him – conceding that he might be able to stay on during a political transition.
In his opening remarks at the summit, UN Secretary General Ban Ki-moon called for the situation in Syria to be referred to the International Criminal Court, saying there can be no impunity for “atrocious crimes”.
Ban Ki-moon said five countries – Russia, the US, Saudi Arabia, Turkey and Iran – were key to finding a political solution, but unless they could compromise it would be “futile” to expect change on the ground.
Earlier, Moscow suggested there were plans to form an international contact group including all the countries Ban Ki-moon mentioned plus Egypt.
The morning session at the UN is hearing from Presidents Barack Obama and Vladimir Putin, as well as Iranian President Hassan Rouhani and French President Francois Hollande, whose country has just carried out its first air strikes against Islamic State (ISIS) militants in Syria.
The threat of ISIS extremists and the flow of Syrian refugees to Europe has added urgency to the search for a deal to end the civil war.
Vladimir Putin has reiterated his support for Bashar al-Assad, who Western countries and the Syrian opposition have said must go.
The Russian president, who has strongly reinforced Russia’s military presence in Syria, has called for a regional “coordinating structure” against ISIS, and said the Syrian president’s troops were “the only legitimate conventional army there”.
Vladimir Putin said Russia would not participate in any troop operations in Syria.
Relations between Russia and the West have been strained over Moscow’s annexation of Ukraine’s Crimea peninsula last year and its support for separatist rebels in Ukraine’s east.
Vladimir Putin will also meet Iranian President Hassan Rouhani and Cuban President Raul Castro on the sidelines of the assembly, the Kremlin was quoted as saying by Reuters.
President Hassan Rouhani – a key regional ally of Bashar al-Assad – says the government in Damascus “can’t be weakened” if ISIS militants are to be defeated.
Secretary of State John Kerry, however, said the efforts were “not yet coordinate” and the US had “concerns about how we are going to go forward”.
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