In a morning call with his counterpart, Kerry also urged full Russian support for efforts to free a mission from the Organisation for Security and Cooperation in Europe held hostage by pro-Moscow militants in the flashpoint city of Slavyansk.
The top US diplomat "expressed continued concern that Russia's provocative troop movements on Ukraine's border, its support for separatists and its inflammatory rhetoric are undermining stability, security and unity in Ukraine," the senior State Department official said.
Kerry's comments came as the Group of Seven top economies and the European Union signaled they would step up economic pressure on Moscow early next week amid fears Russia was preparing an invasion of eastern Ukraine.
Ukrainian Prime Minister Arseniy Yatsenyuk meanwhile claimed Russia violated his country's airspace seven times overnight with an aim "to provoke" it into starting a war.
But Moscow denied any transgression by its warplanes, with Lavrov calling for "urgent measures" to de-escalate the crisis that has plunged East-West relations to their lowest point since the Cold War.