French President Francois Hollande, US Secretary of State John Kerry and British Foreign Secretary William Hague agreed at talks in Paris that there had to be a "precise timetable" for the dismantling of weapons, a statement said.
Western nations also insist there must be consequences if Assad does not implement the terms of the accord but Russian foreign minister Sergei Lavrov has made clear that Moscow will not allow any UN resolution that approves the use of force.
French President Francois Hollande warned on Sunday that a deal to eradicate Syria's chemical arms was "not an end point" and kept the option of military strikes open.
Speaking live on TF1 television, Hollande stressed that the international community must prepare for the possibility of sanctions "in case of non-implementation of the accord" as part of a UN resolution that could be voted on within the next seven days.
Under the terms of the accord, Damascus has one week to put forward a full list of the chemical weapons it possesses and these must be taken away or destroyed within a fixed time limit.
Meanwhile, later on Monday UN Secretary General Ban Ki-moon will present a the much-awaited report by a UN investigation team into chemical weapons in Syria.
Ban He has already revealed that he expects the report to give "overwhelming" confirmation that arms were used in an attack near Damascus on August 21, in which hundreds died.
But the UN team is not allowed to say who carried out the attack, which the West blames on Assad.
Russia's Foreign Minister Sergei Lavrov on Saturday criticised what he called attempts to "retouch" the UN report. Syria's UN envoy, Bashar Jaafari, has also said his government will not accept a "politicized" report.