Yildirim said that solution should involve a new Syrian government "representing all factions".
The talks in Astana took place on January 23-24, with official representatives from Damascus, Russia, Iran and Turkey having taken part, as well as a delegation from the Syrian opposition.
"These are very intense discussions because this is not about a paper; it is about cessation of hostilities, which means saving lives", Staffan de Mistura, the United Nations envoy to Syria.
Turkey's Prime Minister Binali Yildirim said Wednesday this week's Syrian peace talks in Kazakhstan were a "serious diplomatic success".
Turkey, Russia and Iran, the three sponsors of the two-day Syrian talks, made a joint statement at the end of the meeting, stressing their commitment to the sovereignty, independence, unity and territorial integrity of Syria.
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The three states highlighted that the global meeting in Astana is an effective platform for a direct dialogue between the Syrian government and opposition.
The two sides sat at the same table for the opening statements, but spent the rest of yesterday negotiating via mediators.
Russian Federation has sidelined the West with its diplomatic push to find a political settlement to the war in Syria, after its military intervention to support President Bashar Assad turned the tables on the battlefield.
According to both Alloush and Abo Zayd, the opposition provided a paper to Russian Federation detailing ways to monitor and enforce the cease-fire, and Russian Federation has promised to address it within a week, in coordination with Turkey.
Rebel forces are reeling after regime troops, backed by Russian and Iranian firepower, dealt them the biggest blow in over five years of fighting, capturing their eastern Aleppo stronghold last month.
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Representatives from Damascus and the armed rebels in the Kazakh capital were expected to hold their first face-to-face talks since the conflict erupted in 2011, but the rebels refused and mediators had to shuttle between the two sides.
"There's an element of theatrics to it", says Noah Bonsey, the International Crisis Group's senior analyst on Syria.
The talks in Astana were the first negotiations organized by Iran, Russia and Turkey.
"We do not consider the Astana track or trilateral format Iran-Russian-Turkey as a substitute for other tracks or negotiations in Geneva or anywhere else in the world".
There would be joint negotiations with the opposition... The U.S. Ambassador to Kazakhstan did attend the talks as an observer.
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The Kremlin today said the talks on the Syrian crisis in Astana, the capital of Kazakhstan, were successful and will contribute to resuming the Geneva negotiation process.