Russia and Iran, Saudi Arabia's main regional foe, back Syria's government, while Saudi Arabia supports Syrian rebels.
Russia, Iran and Turkey, another rebel backer, have been sponsoring talks, known for their venue, the Kazakh capital of Astana, on local cease-fires and de-escalation zones. A new round starts later this week.
Asked today whether Saudi leaders support the Astana process, Russian Foreign Minister Sergey Lavrov told reporters: "Yes, I think Saudi Arabia is determined to solve the Syria crisis."
Lavrov spoke at a news conference after holding talks with Jordanian Foreign Minister Ayman Safadi.
Earlier this summer, Jordan was involved in three-way talks with Russia and the US on a cease-fire in southern Syria, an area that abuts the Western-backed kingdom.
Jordan has a vital interest in pacifying southern Syria.
The Syrian civil war, now in its seventh year, triggered an exodus of refugees, including hundreds of thousands Syrians who found refuge in Jordan.
Safadi said today that Jordanian-Russian cooperation is important, especially in southern Syria.
Local cease-fires have proven to be the most successful approach to mitigating multi-sided fighting in Syria, which has killed some 4,00,000 people and displaced half the country's population since 2011, he said.
In an apparent dig at the US, Lavrov defended his country's military support for Syrian President Bashar Assad, saying Russia, along with Iran and the Iran-backed Lebanese militia Hezbollah, are there "based on a direct invitation from the legitimate Syrian authorities."
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