Syrian Foreign Affairs Minister Walid Muallem was "clearly trying to disrupt the process... clearly trying to send a message of deterrence to others" when declared that proposals that President Bashar al-Assad were a "red line" for his government were on Saturday, Kerry said.
But Assad's "strongest sponsors", Russia and Iran, have accepted a process that should lead to political transition and a presidential election "at some time", he insisted after meeting Ayrault and foreign affairs ministers from Britain, Italy and Germany and the EU's foreign policy representative.
"If the regime and its backers think they can test boundaries, diminish their compliance in certain areas, or act in ways that call into question their commitment to the cessation, without serious consequences for the progress we have made, they are mistaken," Kerry said.
Ayrault called Muallem's statment a "provocation" and called for the current truce to "fully respected" and humanitarian aid access to be allowed.
Peace talks in Geneva this week will be "difficult" but should lead to a "real political transition", he said.
Kerry said that 600 fighters from the Islamic State (IS) armed group have been killed in the last three weeks and that the Islamists have lost 3,000 square kilometres in Syria.
IS retreats in Iraq, reports
The Iraqi army and local officials on Sunday said that IS had pulled out of Ar-Rutba and Hit in Al-Anbar province, even though they were not under military pressure, apparently indicating problems within its ranks.
IS lost control of the province's capital, Ramadi, in December.
Ayrault also warned Iran that international sanctions could be imposed on it over its recent firing of ballistic missiles, which he judged to be a violation of UN resolutions.