Heading into a crucial week for US plans to launch the strikes, Kerry was to meet Arab League ministers in Paris and head to London before returning to Washington on Monday to continue rallying support at home.
The US Congress returns from its summer break tomorrow to consider President Barack Obama's plans for strikes and UN inspectors are to release a report into an alleged chemical weapons attack by the weekend.
Washington accuses the Assad regime of gassing more than 1,400 people to death in an August 21 attack outside Damascus and wants to launch punitive strikes.
Yesterday, Kerry and French Foreign Minister Laurent Fabius insisted that international support for military action was increasing, after the EU issued a statement calling for "strong" action against Syrian President Bashar al-Assad's regime.
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The EU statement did not call for military action but did condemn the "cynical use of chemical weapons."
More nations were getting behind the need for military action and the number of countries ready to take part was now in the "double digits", he said.
Obama, who is set to address the nation on Tuesday, is facing an uphill battle to convince a sceptical Congress -- and a war-weary US public -- of the need for action.
According to a Washington Post survey, 224 of the current 433 House members were either "no" or "leaning no" on military action as of Friday. A large number, 184, were undecided, with just 25 backing a strike.
The 13 videos were shown to members of the Senate Intelligence Committee on Thursday, according to the panel's website.
US broadcaster CNN also aired the videos, with excerpts showing convulsing children and men sprawled on the floor vomiting and foaming at the mouth.