Russian President Vladimir Putin is to hold rare talks with US President Barack Obama to outline his proposals on the Syrian conflict.
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".
He 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 Mr Ban mentioned plus Egypt.
The morning session at the UN is hearing from both Mr Obama and Mr Putin, as well as Iranian President Hassan Rouhani and French President Francois Hollande, whose country has just carried out its first airstrikes against Islamic State (IS) militants in Syria.
