On Tuesday, however, through its envoy Tom Barrack, Washington said the SDF's original mission of combating Islamic State (IS) group jihadists had "largely expired" after the emergence of a strong US-backed central state.

The SDF and Kurdish security forces had an estimated 100,000 fighters who at their peak controlled vast swathes of oil-rich north and northeastern Syria.

But Arabs within their ranks defected en masse after Syrian President Ahmed al-Sharaa's army on Monday took control of two Kurdish-held provinces, Raqa and Deir Ezzor.

The SDF has now fallen back to parts of its Hasakeh province stronghold in the northeast, around which the Islamist Sharaa's forces have massed.

The Kurdish-led force was formed in 2015 at the instigation of the United States, impressed by the Kurdish fighters who had defeated IS in Kobane in the north, and seeking a reliable partner in the battle against the jihadists, who were defeated territorially in Syria four years later.

According to Syria specialist Fabrice Balanche, the strength of the Kurdish forces -- the SDF and the Asayish domestic security force -- has now fallen to around 50,000, after Arab fighters defected to the government side.

Balanche said the SDF's hard core remains intact, comprising the People's Protection Units (YPG) of some 30,000 members as well as the all-female Women's Protection Units.

Despite denying any links with the Kurdistan Workers' Party (PKK), "it is indeed the PKK that directs the YPG behind the scenes", Balanche said.

YPG units operate under an iron discipline, similar to the model of the PKK banned in Turkey.

- PKK role -

"The YPG was formed in 2011 by PKK veterans," including SDF chief Mazloum Abdi, said Syria analyst Nanar Hawach of the International Crisis Group.

"While the SDF leadership has pursued its own partnerships and political choices, voices from the PKK still play a role in decision-making," he told AFP.

Hawach said Abdi, a civil engineer born in 1967, is a Syrian Kurd who joined the PKK in 1990. He returned to Syria in 2011-2012 to help establish the YPG, and distinguished himself during the battle of Kobane.

The agreement announced on Sunday by Damascus, under which Kurdish fighters would be integrated into state structures, stipulates that the SDF commit to expelling all non-Syrian PKK leaders and members from the country.

"Non-Syrian PKK-affiliated fighters in the SDF are estimated in the hundreds to low thousands," Hawach told AFP.

"Most are Kurds from Turkey, with smaller numbers of Iraqi and Iranian Kurds linked to PKK-affiliated groups.

"While limited in number, they have held significant influence in command and administrative roles, which is why their departure is a central" demand for Damascus.

Following a call by its jailed leader Abdullah Ocalan, the PKK formally renounced its armed struggle against Turkey in May last year, drawing a line under four decades of violence that has claimed some 50,000 lives.

The group maintains a rear base in the Qandil mountains in northern Iraq. The Kurds are spread across Syria, Turkey, Iraq and Iran.

The United States was one of the main suppliers of weaponry to the SDF, and also provided training and funding.

But "heavy weapons were deliberately limited by Washington to manage Turkish concerns", Hawach said.

Turkey shares a more than 900-kilometre (550-mile) border with Syria, and carried out several large-scale operations on its neighbour's territory against the SDF between 2016 and 2019.