Lavrov made the promise at a news conference Monday with EU foreign policy chief Federica Mogherini after talks in Moscow, Censor.NET reports citing AP via U.S. News and Ukrainski Novyny.
Lavrov said Russia, as a 'guarantor of the agreements' signed in Minsk in February 2015, would put pressure on Donetsk and Luhansk to do the same "as soon as Kyiv, eventually, renews or, so to say, starts fulfilling its obligations."
He blamed Ukraine's leadership with attempts to rewrite the Minsk agreements in accordance with their interests, which might stall the whole process, Lavrov said.
An American member of the Organization for Cooperation and Security in Europe's monitoring mission was killed and two others wounded Sunday in eastern Ukraine's separatist-controlled Luhansk region when their vehicle hit a mine.
The U.S. State Department has called on Russia to use its influence on the rebels to improve security in eastern Ukraine.
Both the Russia-backed rebels and the Ukrainian government blamed each other for laying the mine. Fighting in eastern Ukraine has killed more than 9,900 people since it began in 2014.
Related materials: Russian aggression against Ukraine