The Kurdish-led fighters were on Thursday battling to expel IS jihadists from the small town of Baghouz in eastern Syria, the last bastion of their "caliphate" that once controlled large parts of the country.
Putin said Thursday's talks were "constructive and business-like" and that "close coordination" was crucial to ensuring long-term stability in Syria.
However Russia, which wants to hand territory back to Mr Assad, said Damascus would decide the fate of Erdogan's safe zone.
"Our military agencies act in a coordinated way", Erdogan said before starting talks with Russian President Vladimir Putin.
The three leaders also raised doubt on the United States intention to withdraw forces from Syria.
Erdogan said Ankara wanted to move in coordination with Russian Federation on a planned safe zone in northern Syria and added that Syria's territorial integrity could not be established as long as the Syrian Kurdish People's Protection Units (YPG) is not cleared from the area.
"The US withdrawal decision is one of the most important tests ahead of us". The uncertainty over how the decision will be implemented remains.
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It brokered a deal with Russian Federation in September to enforce a demilitarised zone in Idlib.
The territorial integrity of Syria can only be preserved if Kurdish militant forces are driven out of the northern city of Manbij and areas east of the Euphrates River, he added.
".We should not put up with the presence of terrorist groups in Idlib", Putin told Erdogan and Rouhani.
US President Donald Trump's announcement in December that he was drawing down some 2,000 American troops from Syria has also tasked the leaders of Russia, Iran and Turkey with filling the vacuum.
The meeting will be the fourth summit between the countries' leaders since November 2017.
The worldwide anti-IS coalition is set to meet on the sidelines of the Munich Security Conference while US Secretary of State Mike Pompeo will attend a conference on the Middle East in Warsaw.