"Foreign Minister (Sergey) Lavrov has made it clear ... Russia does not intend to fight a war over Syria," Kerry told a hearing in the House of Representatives.
He told the House Foreign Affairs Committee that Lavrov and Russian President Vladimir Putin had made it clear in conversations that "Syria does not rise to that level of ... conflict."
Russia is an important arms supplier to Assad's government and in June said it had stationed 16 warships and three ship-based helicopters in the Mediterranean, its first permanent naval deployment there since the Soviet era.
Moscow announced last week it was sending two warships to the eastern Mediterranean on a regular rotation. US military officials downplayed the move, saying the Russians regularly rotate their warships just as the Americans do. Kerry also downplayed any threat from the Russian vessels.
"Their ships are kind of staying out of the way. They are not threatening that, and I don't think that would be what would happen here," Kerry said, in apparent reference to possible Russian retaliation to potential US action in Syria.