The commander of the Kurdish-led Syrian Democratic Forces (SDF) said Thursday that non-Syrian Kurdish fighters, including members of the Kurdistan Workers’ Party (PKK), will leave Syria if a total cease-fire is reached with Turkey.

The comments from SDF Commander Mazloum Abdi, which were reported by wire service Reuters, mark the first time he has confirmed the presence of non-Syrian Kurdish fighters in Syria.

The withdrawal of these fighters is a central demand from Turkey, which views the PKK and the Syrian Kurdish militias within the SDF, namely the People’s Protection Units (YPG), as security threats.

Abdi stated that while PKK fighters had supported the SDF’s decade-long fight against the Islamic State, there were no internal official ties between the two organizations.

“There is a different situation in Syria; we are now starting a political stage. Syrians must solve their problems themselves and establish a new administration,” he said, adding that it was time for ethnically Kurdish fighters who had come to help fight to return to their areas with their heads held high.”

Turkey, which has backed armed groups in northern Syria, recently seized Manbij from the SDF and is reportedly preparing to attack Kobani. Abdi proposed withdrawing SDF forces from Kobani under the supervision of its longtime partner and backer, the US, to prevent escalation.

Earlier Thursday, a Turkish defense official denied US claims that a cease-fire deal with Syrian Kurdish forces had been reached, refuting comments made by a senior US State Department official.