Beyond that concern, the three leaders will be seeking to safeguard their own interests after investing heavily militarily and diplomatically in Syria.
Iran wants to keep its foothold in the Mediterranean nation neighbouring Israel and Lebanon.
The presidents of Turkey, Iran and Russian Federation yesterday failed to agree on a ceasefire that would forestall a Syrian government offensive in the rebel-held Idlib province which the United Nations fears could cause a humanitarian catastrophe involving tens of thousands of civilians.
"The Tehran summit can produce peace and reconciliation in Syria or it can deepen the mess created by endless bouts of violence mainly instigated by the Assad regime", Ilnur Cevik, a senior adviser to Erdogan, wrote in the Daily Sabah newspaper.
The fate of Idlib province - the last stronghold of the armed opposition - depends on talks between Turkey and Russian Federation and what they will do to ensure the safety of millions of civilians in that region. There are an estimated 10,000 hardcore fighters, including al Qaida-linked militants.
For Russia and Iran, both allies of the Syrian government, retaking Idlib is crucial to complete what they see as a military victory in Syria's civil war after Syrian troops recaptured almost all other major towns and cities, largely defeating the rebellion against Assad.
The streets of Tehran were quiet on Friday, the second day of the Iranian weekend.
"The leaders "rejected all attempts to create new realities on the ground under the pretext of combating terrorism", while expressing determination to stand against separatist agendas aimed at undermining the sovereignty and territorial integrity of Syria and national security of neighboring countries".
For Turkey, the stakes could not be higher. Turkey has accepted 3.5 million refugees from Syria since the start of the war in 2011.
Turkey agreed with Russian Federation and Iran past year to make Idlib a "de-escalation zone" of reduced conflict and sent in army units to erect a string of observation posts along the frontlines between the rebels and the army. "Because America is a danger for humanity and there is a possibility to restrain them".
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"The least the summit can do is to prevent this military war", he said.
Early on Friday, a series of air strikes struck villages in south-west Idlib, targeting insurgent posts and killing one fighter, said Rami Abdurrahman, head of the Britain-based Syrian Observatory for Human Rights.
"Whatever reason there is an attack that has been made or will be made will result in disaster, massacre and humanitarian drama", he said.
Turkey also doesn't want to see another Kurdish-controlled area rise along its border, as it already faces in northern Iraq.
He recounted that the talks between the guarantor states will continue at the level of experts and representatives from the three countries, the representatives of the opposition parties and groups and the representatives from the UN.
All three nations face sanctions from the USA under the administration of President Donald Trump. "We just want to eliminate terrorism in Idlib".
"In a statement Thursday on the eve of a meeting in Tehran (.)", AP reports, "which supports Syria's opposition, the eight nations warned that a full-scale military offensive in Idlib would have "potentially catastrophic humanitarian consequences for civilians".
Trump will chair a U.N. Security Council meeting on Iran during an annual gathering of world leaders in NY later this month.
The eight nations of Europe agree that "only a U.N. -led political process can bring a solution to the conflict that respects the freedom and the dignity of all Syrian people".