Russian Federation has sought to revive diplomacy since its air force helped the Syrian army and allied militias defeat rebels in Aleppo in December, President Bashar al-Assad's biggest victory in six years of war.
The Geneva talks are the fourth to take place under the United Nations auspices and the first since last April.
Meanwhile, the High Negotiation Committee (HNC) - Syria's main opposition group - was expected to meet late Monday with a Russian envoy to discuss calls for Kurdish groups to join the ongoing negotiations. "It is in the interest of all parties who are against terrorism and are committed to a political process in Syria not to allow these attempts to succeed".
Hariri said he believed Moscow was shifting its stance but that he wanted to see constructive support on Tuesday.
Syrian regime strikes targeted a residential building in the northern Ariha town of Idlib on Monday despite a ceasefire brokered by Turkey, Russia and Iran in the Kazakh capital of Astana and came into effect in December. It paved the way for a resumption of United Nations -led mediations after a 10-month hiatus.
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The fourth round of UN-backed intra-Syrian talks between the government and opposition factions kicked off in Geneva on Thursday. "This will not happen until de Mistura resigns", Kassis, the leader of Syria's Movement of the Pluralistic Society, said.
He said the opposition wanted to discuss "the promises they did not keep".
De Mistura, who is treading carefully to keep the talks alive, has so far talked to the two sides separately as he tries to forge an understanding of how to proceed in future rounds.
Opposition sources told Asharq Al-Awsat that the meeting with the Russian delegation would be of high importance, as it would witness discussions about maintaining the fragile ceasefire that was agreed a year ago and Moscow's position on the roadmap stipulated in UN Security Council Resolution 2254, which calls for the formation of a non-confessional transitional administration.