A key challenge is their divided opinions about Syrian President Bashar Assad, who is backed by Russia and Iran and whose government has retaken most of the territory that rebels seized during the war that has killed over 400,000 people.
Western countries condemn Assad for what they call indiscriminate attacks on civilians, and Turkey has been helping insurgents trying to remove him from power.
Still, the leaders meeting in Istanbul hope a cease-fire in Syria's northwestern province of Idlib can provide some momentum for peace efforts. The truce last month prevented a Syrian government offensive on the last rebel stronghold, which many feared would have set off another refugee crisis.
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Putin also spoke to Erdogan on Saturday ahead of the wider talks, the Kremlin said in a statement.
Idlib has been relatively calm since then, although both sides have accused each other of violating the deal. Syrian government forces shelled rebel-held villages in Idlib on Friday, killing seven people in violation of the agreement reached by Russia and Turkey, opposition activists said.
At the Istanbul meeting, Turkish President Recep Tayyip Erdogan is hosting Russian President Vladimir Putin, German Chancellor Angela Merkel and French President Emmanuel Macron.
Besides Idlib, topics on the agenda include access for humanitarian aid, early preparations for the drafting of a constitution and the eventual reconstruction of Syria, which has been in conflict for more than seven years. The ultimate hope is for a political solution that allows millions of Syrian refugees to return home and be safe.
The summit comes amid Turkish threats of a new military operation across the border into northern Syria, in zones held by Syrian Kurdish fighters. Turkey considers the Syrian Kurdish militia, which is backed by the United States, to be terrorists and a part of the Kurdish insurgency within Turkey.
On Friday, Erdogan said Turkey would not allow "terror groups located east of the Euphrates River" to threaten Turkey's security.
Turkey launched two incursions into Syria, in 2016 and 2018, into areas west of the Euphrates, pushing Islamic State militants as well as Syrian Kurdish fighters from its border.