Following international condemnation, a US-brokered, 120-hour ceasefire was put in place. The truce is set to expire at 1900 GMT.
Speaking beside his Russian counterpart Vladimir Putin in Sochi on Tuesday, Erdogan said: "I believe this meeting will benefit the region, which is going through critical days."
Russia and Turkey, which back opposing sides in the Syrian civil war, have forged a delicate alliance in the past year.
Russia has opposed the Turkish operation as an incursion into Syria's sovereign territory. Both sides however support the establishment of civilian safe zones in Syria.
The Kremlin said that Tuesday's summit would focus on "normalizing the situation" in north-eastern Syria.
Turkey intends to set up a 444-kilometre-long and 32-kilometre deep buffer zone along its border with Syria up to Iraq. The military operation is intended to clear the zone.
"Today is the last day for all terrorists in the region to leave," Erdogan said in Ankara ahead of his departure to Russia. "We will resume our offensive much more determinedly if the promises America made to our country are not kept," the Turkish leader said.
The US role in the region has been key, with Washington's surprise announcement at the beginning of the month that it would be withdrawing its troops from the area seen as paving the way for the Turkish offensive.
Over the past week Syrian government troops, accompanied by Russian forces, have entered some north-eastern Syrian towns along Turkey's border, filling a vacuum following the US withdrawal.
Erdogan said he would discuss with Putin the fate of border towns of Manbij, Qamishli and Kobane, all in Ankara's proposed "safe zone."
Erdogan said Turkey had control over more than 2,000 square kilometres of Syrian territory near the Turkish border.
Syrian President Bashar al-Assad described Erdogan as a "thief," saying in comments carried by Syrian state news agency SANA that "he had "robbed the factories, wheat and oil, and today he is robbing the land."
Al-Assad reportedly made the comments while visiting Syrian state troops for the first time in the countryside of the war-torn Idlib region.
The Turkish incursion has drawn other countries into the fray. Erdogan said British Prime Minister Boris Johnson had offered to hold a Syria summit with French President Emmanuel Macron and German Chancellor Angela Merkel.
Germany has proposed the creation of a internationally controlled security zone in Syria.
The Iraqi military said meanwhile that US troops withdrawing from Syria were not permitted to stay in Iraq and will move outside the country.
A convoy of US troops had crossed from Syria into Iraq's northern province of Dohuk, in Iraqi Kurdistanm, on Monday.
"There is no approval for these troops to stay inside Iraq," the Iraqi military said.
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