Moscow (AFP) - After talks with Moscow's top diplomat, Syria's main opposition group insisted Friday that Russia is "not clinging" to President Bashar al-Assad.

The head of Syria's National Coalition, Khaled Khoja, met Thursday with Russian Foreign Minister Sergei Lavrov as part of a fresh push by Moscow to find a way out of the four-year civil war that has cost some 240,000 lives.

Moscow -- one of Assad's few remaining backers -- is pushing a plan for a broader grouping than the US-led coalition fighting the Islamic State (IS) group, to include Syria's government and its allies.

But Khoja -- in Moscow for the National Coalition's first talks there since February 2014 -- reiterated that Assad must go immediately and hinted that Russia's support for the strongman may be wavering.

"We have found that the Russian authorities are not clinging to Bashar al-Assad personally, but rather they’re clinging to the Syrian state, its territorial integrity, and the preservation of its institutions," Khoja told journalists at a press conference.

A spokeswoman for Russia's foreign ministry said in response that Moscow's position remained unchanged.

"We have always said that we do not support Assad in a personal capacity but that we support the legitimately elected president of Syria," spokeswoman Maria Zakharova told AFP.

The ministry said in a statement that Russia was pushing the National Coalition -- Syria's main opposition group in exile -- to talk to other parties in the fragmented opposition about the creation of a cohesive negotiating platform for talks with the authorities.

The meeting Thursday is part of a broader diplomatic flurry that saw Saudi Arabia's foreign minister Adel al-Jubeir fly into Moscow on Tuesday, on the back of a three-way Russian-Saudi-US meeting in Doha earlier this month.

The top diplomat for Saudi Arabia, a key backer of the Syrian opposition, rejected calls to work with Assad against IS after a meeting with Lavrov.

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As part of the push, Lavrov also met on Friday with the head of a newer grouping of Syrian opposition figures known as the Cairo Conference Committee.

The leader of the group Haytham Manna said after the talks that political change needed to happen for the fight against extremists in Syria to be effective.

"The Russians believe that the most urgent thing is the fight against terrorism but we believe that to win the fight against terrorism, political change is a prerequisite," Manna told AFP.

"We agreed that the fight against terrorism and the political process should happen together."

On Wednesday, Russia's top Middle East envoy met in Moscow with Saleh Muslim, the head of the Syrian Kurdish Democratic Union Party (PYD).