PARIS—The number of countries ready to take military action in Syria has reached "double digits," U.S. Secretary of State John Kerry said Saturday after European Union foreign ministers agreed there was strong evidence the regime of Bashar al-Assad was behind the alleged use of chemical weapons against rebels.

Mr. Kerry was speaking at a joint press conference with French Foreign Minister Laurent Fabius that sought to address deep skepticism among lawmakers and the public in both countries. Washington and Paris are...