Saudi Arabia backs the Turkey-backed process of negotiating gradual local cease-fires in Syria, including the establishment of "de-escalation zones," Russian Foreign Minister said Monday.

Sergey Lavrov spoke after a meeting with his Jordanian counterpart and a day after talks with Saudi leaders.

Russia and Iran back Assad regime, while Saudi Arabia supports Syrian oppposition. Russia, Iran and Turkey, another opposition backer, have been sponsoring talks in Kazakhstan on gradual cease-fires and de-escalation zones. A new round in the Kazakh capital, Astana, starts later this week.

Lavrov says Saudi Arabia assured him that it "supports this process and will cooperate in terms of creating de-escalation areas and other initiatives under the Astana process."

Lavrov and his Jordanian counterpart, Ayman Safadi, said the Astana approach is the most practical.

On May 4, Russia, Turkey and Iran signed a deal in the Kazakh capital Astana to establish de-escalation zones in Syria.

The May 4 de-escalation zone agreement envisages the halt of hostilities between Assad regime forces and moderate opposition groups within the zones as well as the creation of conditions for humanitarian access, medical assistance, the return of displaced civilians to their homes and the restoration of damaged infrastructure. The guarantor states previously agreed to take all measures necessary to continue fighting Daesh, al-Nusra and other terrorist groups both within and beyond the de-escalation zones.

Syria's conflict evolved from a bloody crackdown on protests in 2011 to a devastating war that has drawn in world powers, including Russia and a U.S.-led international coalition. Since then, more than 250,000 people have been killed and in excess of 10 million displaced, according to the U.N.