Lavrov told Hamas politburo chief Khaled Mashaal in a phone conversation that the Palestinians organization must stop the "unconscionable firing of rockets from the Gaza Strip into southern Israel."
Mashaal said that the Hamas leadership has decided to "maintain the calm, and is not interested in escalating the tension. He promised that his organization would take "appropriate measures to prevent the rocket fire from Gaza."
Lavrov and Mashaal met in early February, when the Hamas leader visited Moscow.
The firing of rockets from the Gaza Strip has increased recently. The latest rocket hit the Eshkol Regional Council on Monday evening, without causing any injuries or damage.
Monday's rocket followed weeks of rising tensions on the Gaza front, which culminated in a fire exchange that left Major Eliraz Peretz and Staff Sergeant Ilan Sviatkovsky dead on Friday.
Following the lethal incident and increased rockets attacks in recent weeks, the Israel Defense Forces has been on high alert for the holiday of Passover ,in preparation for another possible escalation.