The commander of Syrian Kurdish-led forces in Syria said in an interview on December 19 that Kurdish fighters who came to the country from around the Middle East to fight for his militia will leave if Turkey agrees a total ceasefire on clashes taking place in northern Syria.

"There is a different situation in Syria [following the fall of the Assad regime two weeks ago], we are now starting a political stage. Syrians must solve their problems themselves and establish a new administration," Mazloum Abdi, who leads the Syrian Democratic Forces (SDF), told Reuters.

He added: "We are now preparing, after a total ceasefire between us and the Turkish forces and their affiliated factions, to join this stage.

"Because there are new developments in Syria, it is time for the fighters who helped us in our war to return to their areas with their heads held high."

Since Syria moved into its post-Assad era following the Turkey-endorsed early December lightning offensive by armed groups that brought down president of 24 years Bashar al-Assad—who fled to Moscow—Ankara has driven a stepped-up military push against the US-allied SDF in the north and northeast of Syria. The Kurds exercise de facto control over a substantial part of the country in these regions, sometimes referred to as Rojava.

The withdrawal of non-Syrian Kurdish fighters from Syria is a major demand of Turkey. It designates the SDF a “terrorist” entity that it does not distinguish from the Iraq-based Kurdistan Workers’ Party (PKK). The PKK has waged a 40-year armed insurgency against Turkey since 1984.

Abdi has never before confirmed that non-Syrian Kurdish fighters are in Syria amid the ranks of his forces. Abdi in the interview conceded that fighters of the PKK—listed as terrorist by Turkey, the US, EU and the UK—had come to Syria, but at the same time insisted the SDF has no organisational ties to the group.

Non-Syrian fighters, he said, who hailed from countries including Turkey, Iraq and Iran, had helped the SDF battle Islamic State over the last decade. In bringing down the self-declared Syrian and Iraqi caliphate of the Islamic State, the SDF, which is dominated by the Kurdish YPG militia, served as the main fighting force in an alliance with Washington. The SDF and the US say there is still work to do in stamping out remnants of Islamic State and ensuring it is not resurgent in the new Syria.

Some of the non-Syrian fighters had returned home over the years, but others stayed to continue the fight against Islamic State after the fall of the caliphate, Abdi added.

The US has this week been mediating to stop the growing attacks made by Turkey and the Syrian Arab groups it supports on the SDF.

There is some confusion as to whether a temporary ceasefire until the end of this week prevails. The US has said there is one, but some Turkish sources who have briefed newswires have denied that this is the case. Ankara has also stated that if concerns over the Kurdish forces in northern Syria are addressed “properly” by the new administration in Damasus, there will be no need for a military intervention.

In further comments, Abdi, who also gave an interview to FRANCE 24, turned to a possible attack Turkey and its allies in Syria might direct at the Syrian city of Kobani, or Ayn al-Arab, a large population centre located by the Syrian-Turkish border.

The SDF has proposed withdrawing its forces from the Kobani area, in favour of an internal security force with US forces present "to supervise this area – provided that there is a complete truce", according to Abdi.

"On the other hand, we are preparing ourselves to repel any attack if it happens," he added.

The attacks on the Kurdish forces are being led by the Syrian National Army (SNA), created and funded by Turkey and a force that took part in the offensive that toppled Assad.

In the US, some senators have threatened to hit Turkish President Recep Tayyip Erdogan and Ankara with sanctions if Erdogan does not stop the SNA attacks.

Turkey has rejected US President-elect Donald Trump’s contention that it orchestrated the offensive and “unfriendly takeover” that spelled the end for Assad, but Erdogan on December 18 said during a speech to a gathering of top Turkish scientists that Turkey cannot be “confined” to its borders and that its activities in other countries are part of Turkey’s “sacred journey”. Events in Syria were a reminder, he added, that “Turkey is bigger than Turkey itself.”

The extent of Turkey’s influence over the emerging new administration in Syria is hotly debated, with some claims that Ankara plans to run the country through a “parallel structure”.

Turkey and Israel, meanwhile, have traded barbs over land grabs in Syria they accuse each other of making since Assad fell and his forces dissolved.