The agreement was reached after President Barack Obama spoke with his French counterpart Francois Hollande and British Prime Minister David Cameroon.
"They agreed to work closely together, and in consultation with Russia and China, to explore seriously the viability of the Russian proposal to put all Syrian chemical weapons and related materials fully under international control in order to ensure their verifiable and enforceable destruction," the official said on condition of anonymity.
The efforts will begin today at the United Nations, and will include a discussion on elements of a potential UN Security Council Resolution, the official said.
"Diplomacy is our first resort. And we have brought this issue to the Security Council on many occasions. We have sent direct messages to Syria.
"And we've had Syria's allies bring them direct messages: 'Don't do this. Don't use these weapons,' all, to date, to no avail," Kerry said during a Congressional hearing.
A day earlier, Kerry had made a casual remark asking Syria to hand over its chemical weapons to the international community so that they could be destroyed.
"And that, of course, would be the ultimate way to degrade and deter Assad's arsenal, and it is the ideal way, to take this weapon away from him," Kerry said.
"Assad's chief benefactor, the Russians, have responded by saying that they would come up with a proposal to do exactly that. We have made it clear to that this cannot be a process of delay. This cannot be a process of avoidance," he said.
"It has to be real. It has to be measurable, tangible. And it is exceedingly difficult, I want everybody here to know, to fulfil those conditions. But we're waiting for that proposal," he added.
"And if the United Nations Security Council seeks to be the vehicle to make it happen, that cannot be allowed to simply become a debating society," he asserted.
