Fierce fighting is continuing in the area surrounding the Northern Syrian town of Ras Al-Ain as Turkish troops and locally-based Kurdish-led Syrian Democratic Forces, known as SDF, clash following last week's withdrawal of United States troops from the region.

Anadolu, Turkey's official news agency, said on Sunday that Turkey-backed Syrian forces have advanced into the center of a Syrian border town, Tal Abyad, on the fifth day of the Turkey's military offensive against Kurdish fighters in Syria.

Turkey accuses the Kurds, who have been key allies for the West in the battle against Islamic State, or IS, of being terrorists. It launched a fierce offensive against them as soon as US President Donald Trump announced the US withdrawal.

More than 100,000 people have been displaced, with around 50 killed, and after days of air bombardment, Turkey claims to have taken control of the town, although the SDF disputes this.

Turkey's Defense Ministry tweeted: "Ras al Ain's residential center has been taken under control through the successful operations in the east of the Euphrates (river)", but SDF said that they had only managed to enter one neighborhood and were being pushed back.

If the Turks have been successful, it would be their most strategically important gain so far, in addition to several smaller towns and villages that have already fallen under their control.

A local human rights group says video footage has emerged of Kurdish civilians including one of the country's leading female politicians being killed by Turkish-backed militias.

Hevrin Khalaf, the secretary general of the Future Syria party, was among those killed on Saturday. Previously the 35-year-old had been involved in high-level diplomatic negotiations with overseas representatives.

"This is a clear evidence that the Turkish state is continuing its criminal policy towards unarmed civilians," said a statement from SDF's political arm.

Turkey's actions have drawn strong criticism from the international community but President Recep Tayyip Erdogan remains defiant, warning the European Union in particular that he would trigger a new influx of refugees and "open the gates" if anyone called his offensive "an invasion".

In addition to the humanitarian crisis, the situation is of concern because of the prospect of IS prisoners and suspects currently guarded by Kurdish forces being freed.

IS has already attempted to exploit the situation, detonating a car bomb outside a prison in Hasaka in Northeastern Syria, to try and spring some of its detainees and also divert the efforts of the already-overstretched Kurdish security forces.

Turkey wants to drive the Kurds out of the area to set up what it calls a "safe zone" to house 3 million refugees from Syria who are currently in Turkey.

On Saturday, senior SDF official Redur Xelil made a televised address saying that the US had a "moral obligation" to help protect them. "We don't want them to send their troops to the frontlines... all we want is that they close the air space to Turkish planes and they can do this easily."

France has halted arms sales to Turkey and Britain said Turkey's actions weakened the international fight against IS. US president Trump has also issued stern warnings about Turkey's behavior but Erdogan has brushed off criticism, saying such talk "will not stop it, no matter what anyone says".