The two top diplomats are in daily contact on the matter and sealed a deal in Geneva last weekend aimed at dismantling the Damascus regime's arsenal of these types of banned arms.
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While welcoming his Dutch counterpart Frans Timmermans to the State Department, Kerry told reporters he had had a fairly long phone conversation with Lavrov earlier in the day.
"We talked about the cooperation which we both agreed to continue to provide, moving not only towards the adoption of the OPCW (Organization for the Prohibition of Chemical Weapons) rules and regulations, but also a resolution that is firm and strong within the United Nations," Kerry said.
"We will continue to work on that," he added.
Timmermans, meanwhile, said the Netherlands and the United States were "exactly on the same page."
"In the UN, we see eye to eye as to the content of the United Nations Security Council resolution, which should be very firm on making sure that Assad, who doesn't have a track record of actually doing what he promises, does what he has promised now," he said, referring to Syrian President Bashar Assad.
On Thursday, Kerry said the UN Security Council must be prepared to agree to a binding resolution on Syria's chemical weapons next week.
The five permanent members of the panel – the United States, China, Russia, France and Britain – have been wrangling over the text of the resolution since Monday in an effort to find common ground.
Russia, a key ally of Damascus, opposes all references to a possible use of force.
Just as Kerry and Timmermans were speaking, the Organization for the Prohibition of Chemical Weapons said it had received initial details on Syria's program and arsenal, which it has been tasked with dismantling.
The world's chemical weapons watchdog, which enforces the Chemical Weapons Convention that Syria has applied to join, has repeatedly postponed a meeting of its Executive Council to discuss the practicalities of how to dispose of Syria's chemical weapons.
A new date for the meeting has not yet been set.
Diplomatic sources said that a draft text to be discussed at the meeting had not yet been agreed upon by the United States and Russia.
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