The U.S. has long insisted that Assad must be replaced through a negotiated political transition. The rise of a common enemy, the Islamic State in Iraq and the Levant (ISIL), appears to have softened the West's stance toward him.
Marie Harf, State Department spokeswoman, said later on Sunday that Kerry was not specifically referring to Assad, with whom the U.S. would never negotiate.
But Washington's allies appeared to be caught off-guard by Kerry's comments. France, a major U.S. ally, said its position was unchanged and that Assad could not be part of a negotiated solution in Syria.
Asked by French television channel Canal+ whether he regretted Kerry's comments, French Prime Minister Manuel Valls said Monday: "Yes, of course." Assad, he noted, was "responsible for tens of thousands of deaths."
"There will not be a political solution, there will not be a solution for Syria as long as Bashar al-Assad stays, and John Kerry knows it," Valls said.
When asked about Kerry's remarks on Monday, Mevlut Cavusoglu, the Turkish foreign minister, called Assad's government "the reason for all the problems" in Syria.
"What is there to negotiate with Assad?" he said. "What will you negotiate with a regime which has killed more than 200,000 people and used chemical weapons? What result is achieved through negotiations so far today?"
Al Jazeera and wire services