According to the statement, Lavrov warned Kerry about the "worsening situation," which he blamed on the Ukrainian side's "constant attacks on populated settlements in breach of the Minsk protocol."
The statement added that both sides agreed on the need for an "immediate halt to artillery attacks" and the removal of heavy weapons from the front line, a point found in the Minsk protocol which was signed in September 2014.
Lavrov stressed that "Russia is ready to do everything in its power to encourage the parties to a peaceful solution," but the foreign minister also called on his American counterpart to discourage the Ukrainian government in Kiev from "betting on a military resolution."
While the statement has Lavrov accusing Ukraine of shelling populated areas, Saturday's rocket attack on the Ukrainian-held city of Mariupol is reported to have come from separatist-held territory according to the OSCE. The OSCE's report, published on the organization's official website, listed approximately 20 dead, with an additional 75 wounded as a result of the morning bombardment by BM-21 Grad multiple rocket launchers.
According to the UN, over 5,000 people have lost their lives due to the conflict which began last April.