France, Britain and the United States have said they will seek a "strong and robust" UN resolution that sets precise and binding deadlines on removal of Syria's chemical weapons, the office of the French President Francois Hollande said.
Monday's statement follows talks between foreign ministers of the three countries and Hollande in Paris - two days after Moscow and Washington reached a deal on chemical weapons that could avert US military action.
The three powers also agreed at talks in Paris that President Bashar al-Assad would face "serious consequences" if he fails to comply with the UN resolution, French Foreign Minister Laurent Fabius said.
US Secretary of State John Kerry did not use the word "serious", saying: "If Assad fails to comply with the framework we are all agreed that there will be consequences".
Kerry, who agreed the terms of the weapons handover with his Russian counterpart in Geneva on Saturday, said the allies were committed to keeping up the pressure on Assad.
Referring to the UN resolution, Kerry stressed it was "crucial" that it be "enforced", and that it has to be "strong", "forceful", "transparent", and "timely".
"If the Assad regime believes that this is not enforceable and we are not serious, they will play games," he said.
Fabius announced there would be a major international meeting with leaders of the opposition Syrian National Coalition on the sidelines of the UN General Assembly in New York next week.
"We know that in order to negotiate a political solution, there has to be a strong opposition," Fabius said.
French officials said Russia had been invited to the conference.
Kerry, British Foreign Secretary William Hague and Hollande have also agreed to continue to work toward a political solution with the Syrian opposition.
The US secretary of state stressed that the allies were "committed to the opposition" and said Assad had "lost all legitimacy to be possible to govern his country".
The signal of support for the rebels came in reaction to criticism of the chemical weapons deal from opposition leaders, who fear it could consolidate Assad's grip on power.
The pact came after Washington led calls for military action in response to an August 21 chemical attack on the outskirts of Damascus blamed by the US - which says more than 1,400 people were killed - and others on the Syrian government.
On Sunday, Hollande said "the military option must remain" to force Syria to give up its chemical arsenal.
In-depth coverage of escalating violence across Syria
US and Russian officials reached an ambitious agreement over the weekend calling for an inventory of Syria's chemical weapons programme within a week, with the programme eradicated by mid-2014.
The UN's chief weapons inspector submitted his team's report on the August attack on Sunday.
The August 21 attack unfolded as a UN chemical weapons team was in Syria to investigate earlier reported attacks.
After days of delays, the inspectors were allowed access to victims, doctors and others in the Damascus suburbs afflicted by the poison gas.
The Security Council is due to take up the report in a closed session on Monday.
The Assad regime insists that the attack was carried out by rebels.
The inspection team led by Swedish expert Ake Sellstrom was mandated to report on whether chemical weapons were used and which ones - not on who was responsible.