France has been pushing for a tough Security Council resolution and has blamed the Syrian government for the sarin attack on Damascus suburb of Ghouta on August 21.
Fabius, who met with British and American counterparts Monday, will send together with Britain a draft resolution which demands a threat of sanctions if President Bashar al-Assad does not comply with the disarmament plan agreed over the weekend in US-Russian talks.
However Lavrov on Monday said any resolution using threats was detrimental to Syria's chemical disarmament plan and to a long-term peace plan for the war-torn country, where 110,000 people have been killed over the past 30 months.
He said the resolution must simply support the programme of the Organisation for Prohibition of Chemical Weapons, and offer to provide additional workers for securing Syria's chemical sites.
Russia had insisted the August 21 attack was a provocation by the rebels, saying using chemical weapons was not in Assad's interests.
But France, the United States and Britain put the blame squarely on the regime.
The United States had said the attack killed more than 1,400 people and UN chief Ban Ki-moon condemned it as a "war crime". However the United Nations experts who visited the site did not assign blame to either side.