The Turkish president has threatened to press ahead with an operation against Kurdish-led forces in Syria “even more strongly” if promises made by the US regarding the withdrawal of fighters have not been met by the time a five-day ceasefire expires.

Up to 1,300 fighters from the Syrian Democratic Forces (SDF) are yet to vacate Ankara’s proposed border “safe zone”, as per the terms of a ceasefire announced by the US vice-president, Mike Pence, in Ankara last week, Recep Tayyip Erdoğan told reporters before flying to Russia.

“There is no place for the [Kurdish fighters] in Syria‘s future. We hope that with Russia’s cooperation, we will rid the region of separatist terror,” he said.

Erdoğan was meeting withVladimir Putin in the Black Sea city of Sochi on Tuesday for talks expected to determine the size and scope of Turkey’s planned buffer zone, hours before the pause in fighting ends at 10pm local time (1900 GMT).

Trump’s withdrawal of the remaining 1,000 US special forces from Kurdish-held Syria means Moscow and Ankara have emerged as the two main foreign players in Syria’s long war. The two leaders were all smiles during handshakes for media on Tuesday afternoon – a stark contrast to the grim expressions worn by all parties during the visit of Pence and the US secretary of state, Mike Pompeo, to Turkey last week.

Turkish troops, allied Syrian rebel proxies, the SDF, and soldiers belonging to both the Syrian president, Bashar al-Assad, and his Russian allies are all present in the border stripafter Donald Trump announced he would withdraw US troops, paving the way for Ankara to launch an attack on the SDF on 9 October.

As a result of the Turkish offensive, Syria’s Kurdish officials struck a deal with Assad, their former enemy, for military reinforcements in the border area.

Russia has emerged as Syria’s major powerbroker, with powerful sway on all sides. Turkey has suggested it wants Moscow to persuade Damascus to cede it control over a major chunk of territory in the north-east, which would break up Kurdish control.

Kurdish officials, however, are hoping Russia can negotiate with Assad to help preserve some of the autonomy they have carved out for themselves during Syria’s civil war.

Assad has repeatedly vowed to reunite his entire country under Damascus’s rule. In a symbolic visit to the north-western province of Idlib on Tuesday – territory the regime occupies for the first time in years – he called Erdogan “a thief” and said he was ready to support any “popular resistance” against Turkey’s invasion.

“We are in the middle of a battle and the right thing to do is to rally efforts to lessen the damages from the invasion and to expel the invader sooner or later,” he told troops, adding that Kurdish fighters would be granted an amnesty if they return to the Syrian government’s wing.

Russia has previously demanded that Turkey respect Syria’s territorial integrity and suggested Assad has the final say on the presence of Turkish troops in the country. Putin is thought to have sought commitments from Erdoğan on Tuesday but no details of the leaders’ meeting were immediately forthcoming.

“The most important thing for us is achieving long-term stability in Syria and the region,” President Putin’s foreign policy adviser, Yuri Ushakov, said ahead of the talks on Tuesday. “We believe this can only be achieved by restoring the unity of Syria.”

Despite the ceasefire, intermittent fighting between the SDF and Ankara’s Syrian rebel proxies has continued. At least 120 civilians in Syria and 20 in Turkey have died as a result of the almost two-week old assault.

Turkish forces in the northern Syrian town of Tel Abyad. Photograph: Xinhua/Barcroft Media

Kino Gabriel, an SDF spokesman, confirmed over the weekend that all its fighters had evacuated the town of Ras al-Ayn, one of the two border towns bearing the brunt of the Turkish attack, as part of the US-brokered pause.

Redur Khalil, another senior SDF official, also said that following the evacuation of the remaining civilians and fighters from Ras al-Ayn, his fighters would pull back from the strip of land between the town and Tel Abyad, which is also under Turkish attack.

Ankara has stuck to its original proposal of a 270-mile long (440km), 20-mile deep buffer zone from the Euphrates river to the Iraqi border, but the SDF has only acknowledged the 75-mile area between Ras al-Ayn and Tel Abyad.

The US-brokered agreement struck last Thursday did not specify the zone’s size, where Turkey also plans to repatriate up to 2 million of its 3.6 million Syrian refugee population.

Previous agreements between Washington and Ankara over a “safe zone” along the Syria-Turkish border have floundered over diverging definitions of the area.

Trump’s decision to withdraw from Syria, which effectively green-lighted the Turkish attack, has been widely condemned as a betrayal of the US’s military partner in the five-year-long campaign to defeat Islamic State.

Ankara, however, has long maintained that the main Kurdish unit within the SDF is indistinguishable from the outlawed Kurdistan Workers’ party (PKK), which has waged war against the Turkish state for decades.