The resolution comes against a backdrop of deadlock among the veto-wielding members of the Security Council.
While Russia supports Syrian President Bashar al-Assad, the US, UK and France have insisted that the President must step down as part of any deal to end the war.
The Russian resolution, however, called for rapid access for the delivery of humanitarian aid all over Syria.
BBC said the draft text also supported a political process to end the conflict, with talks between the government and opposition, brokered by Russia and Turkey said to be due in January in Kazakhstan.
The truce, which began barely 48 hours, has held in most places.
But there have been a number of clashes and air strikes while several groups including the Islamic State and Al-Nusra Front are excluded from the ceasefire deal.
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