"The Islamic Republic believes the only solution to the Syrian crisis is political and not a military solution," Rouhani said in a televised opening address.
"We continue to support the inter-Syrian dialogue and underline our determination to fight the terrorism of Daesh, Al-Qaeda, and other related groups."
"I emphasize that the fight against terrorism will continue until it is completely eradicated in Syria and the region in general," he added.
Rouhani said the illegitimate presence of US forces in Syria should end immediately.
Iran would continue its support for Syria’s legal government, he added.
The Iranian president also condemned “unilateral and inhumane sanctions” imposed by the US on Syria, calling the move an act of “economic terrorism” that violates international law, human rights, and the sovereignty of Syria.
Putin told his counterparts that there was a need for peaceful dialogue between the opposing forces in Syria’s war.
Putin said hotspots of terrorism still remain in Syria’s Idlib and other regions.
“An inclusive inter-Syrian dialogue should be actively promoted within the framework of the constitutional committee in Geneva. I propose to support this process, to help the participants meet and start a direct dialogue,” Putin said.
In Syria’s nine-year-old war, Russia and Iran are the main foreign supporters of President Bashar al-Assad’s forces, while Turkey backs militants. Under a diplomatic process dating back to 2017, they agreed to work to reduce fighting.
After worsening violence displaced nearly a million people, Turkey and Russia agreed in March to halt hostilities in northwest Syria’s Idlib region.
Erdogan told the videoconference that the priority for Syria is a lasting solution to the conflict, “achievement of calm in the field and the protection of Syria’s political unity and territorial integrity”.
“We will continue to do all we can so that our neighbor Syria finds peace, security and stability soon,” he said.
The talks are the first since September in the so-called Astana format, in which the three powers discuss developments in Syria.
The three president also issue a joint statement in which they “expressed their determination to stand against separatist agendas aimed at undermining the sovereignty and territorial integrity of Syria as well as threatening the national security of neighboring countries.”
They also voiced “their opposition to the illegal seizure and transfer of oil revenues that should belong to the Syrian Arab Republic.”
The statement noted that “the Syrian conflict could only be resolved through the Syrian-led and Syrian-owned, UN-facilitated political process in line with the UN Security Council Resolution 2254.”
It also highlighted the need to “facilitate safe and voluntary return of refugees and internally displaced persons to their original places of residence in Syria, ensuring their right to return and right to be supported.”
AFP and Reuters contributed to this story.