Speaking in London ahead of a conference on the Syrian humanitarian effort, Kerry said he had called Russian Foreign Minister Sergei Lavrov for a "robust" discussion.
In Geneva yesterday, UN envoy Staffan de Mistura suspended attempts to begin a dialogue between Bashar al-Assad's regime and the Syrian opposition.
Alongside Britain's Foreign Minister Phillip Hammond, Kerry read out sections of UN Security Council resolution 2254, passed in December, calling for an immediate ceasefire.
"Russia has a responsibility, as do all parties, to live up to it," he said.
Kerry also said that both parties to the conflict - the rebels and the regime and its allies - must allow access to besieged areas for humanitarian aid.