Turkey and Russian Federation, who are backing opposing sides in the Syrian conflict, only said they agreed on the need for a cease-fire.
"We believe that Assad can not actually enhance the national unity in the country", Cavusoglu said.
The Office of Coordination of Humanitarian Affairs says the situation has deteriorated in eastern Aleppo since November 24, after pro-government forces took control of some areas.
Turkish President Recep Tayyip Erdogan caused waves in Russian Federation this week with remarks suggesting that Turkey's military actions in Syria, where it has a small presence ostensibly to counter IS and contain the gains of Kurdish foes, aims to topple the Assad regime.
Russian Federation and Iran are the Syrian regime's chief allies in the war against opposition rebels who are, in turn, supported by Turkey, various Gulf states and in part by the Central Intelligence Agency.
Turkey has embarked on an ambitious military operation inside Syria since August, supporting opposition fighters who have so far retaken Jarabulus, Al Rai and the symbolically important town of Dabiq from Islamic State (IS) jihadists.
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When Ankara first threw its support behind the Syrian rebels in 2011, offering them bases inside Turkey and becoming the main conduit for weapons flowing in from their Gulf benefactors, Erdogan cheerfully predicted that victorious Turkish leaders and their Syrian allies would "inshallah" be praying in the famed Ummayad Mosque in Damascus "in the shortest time possible".
"Our President (Recep Tayyip Erdogan's) position on (Syrian President Bashar) Assad is clear".
"These people have been besieged for almost 150 days now and most simply don't have the means to survive for much longer". Erdogan had on Tuesday said Turkey launched the offensive to "put an end to the rule of the tyrant Assad who carries out state terror, not for anything else". Erdogan said that Turkey has no territorial claims in Syria, but instead wants to hand over power to the Syrian population, adding that Ankara is seeking to restore justice.. No mention has been made by either side over whether they discussed Erdogan's remarks.
Turkey's efforts to provide humanitarian aid to Aleppo were also discussed during the meeting. Previous attempts to open up such corridors have broken down, however, as a result of the US-backed Islamist militias shelling them and firing upon civilians attempting to escape.
The Russian military says the Syrian government has taken over a city just outside of the capital after a rebel retreat.