The resolution, drafted by Russia, also calls for rapid access for humanitarian aid to be delivered across the country.
The ceasefire, which began just over a day ago, has mostly held.
But Syria’s main rebel alliance had threatened to abandon the truce by 18:00 GMT if the government continued to attack areas under its control.
The Free Syrian Army (FSA) issued the ultimatum to Russia – Syria’s key ally – amid reports of intense bombardment by government forces on the rebel-held Wadi Barada area of Damascus, which the rebels say is in breach of the truce.
Shelling on the area concerned ceased just minutes before the deadline, the group’s legal adviser, Osama Abu Zeid, said.
The truce applies across Syria but does not cover certain rebel groups including the jihadists of so-called Islamic State (IS) and Jabhat Fateh al-Sham (JFS), and the Kurdish YPG militia.
Earlier on Saturday, the FSA said that, following statements from Russian officials, it was “surprised” to find that its version of the agreement differed from that of the government.
The UN resolution comes against a backdrop of deadlock among the veto-wielding members of the Security Council, with Russia supporting Syrian President Bashar al-Assad and the US, UK and France insisting he must step down as part of any deal to end the war.
Russia and Turkey also back opposite sides in the conflict, with Turkey supporting the rebellion against Mr Assad.
Read more on BBC