Talks on the Syrian crisis were held in Moscow on Tuesday between UN / Arab league envoy Kofi Annan and President Vladimir Putin.
Afterwards, Mr Putin said Russia still backed Mr Annan's six-point peace plan, which called for a ceasefire and talks between the government and opposition.
The BBC reports Russia and China have consistently refused to back any measures that hint at intervention in Syria, or ask for Mr Assad to step down.
Western nations want them to back tougher measures to stop the fighting.
Moscow says it does not support President Bashar al-Assad, but that it will not agree to any deals that are conditional on his leaving power.
The UN has until Friday to renew a mandate for its observers in Syria.
On Monday, Foreign Minister Sergei Lavrov said Russia would block moves at the UN Security Council to extend the mandate if Western powers did not stop resorting to "blackmail" by threatening sanctions against Damascus in their draft resolution.
Russia has put forward a draft resolution, which would prolong the UN mission in Syria for 90 days.
