Lavrov, during a telephone conversation with US Secretary of State John Kerry, emphasised the necessity to de-escalate the situation in Ukraine, "firstly to cease the military operation against protest participants and stop aggressive actions of radical nationalists of the Right Sector," Xinhua quoted the foreign ministry as saying in a statement published on its website.
Russia called for the US attention to proposals of the Party of Regions and public movements of the southeast region regarding the beginning of "all-Ukraine national dialogue and constitutional reform," it added.
Kerry assured that Washington would use its capabilities to encourage Kiev authorities to undertake measures to decrease tensions.
On Saturday, pro-Russia fighters in east Ukraine said they have not ruled out releasing kidnapped Ukrainian army officials and international mediators in exchange for the release of their own men.
Slaviansk has become a flashpoint in the conflict between pro-Russia protesters and Ukrainian authorities in eastern Ukraine, where pro-Russia fighters have occupied a string of towns.