Between them the Damascus government and the Syrian Democratic Forces control most of the country, after a series of Russian-backed victories over rebel groups in recent months saw the government reassert its authority in the south.
The delegation from the SDF’s political wing is discussing the future of the autonomous administrations it has set up in areas of northern and northeastern Syria under its control, the alliance official said.
“A delegation from the Syrian Democratic Council is paying a first official visit to Damascus at the invitation of the government,” the council’s Arab co-chair Riad Darar said.
“We are working towards a settlement for northern Syria.
“We hope that the discussions on the situation in the north will be positive,” Darar said, adding that they were being held “without preconditions”.
The SDF controls more than 27 percent of Syrian territory, according to the Syrian Observatory for Human Rights, a Britain-based monitoring group.
It holds not only Kurdish-majority areas along the northern border with Turkey but also the Arab-majority city of Raqqa, made infamous by the Islamic State group as its former de facto Syrian capital.
SDF fighters captured the city with support from a US-led coalition last October in their most high-profile victory of the war.
The SDF has since lost the Kurdish enclave of Afrin in northwestern Syrian to Turkish-backed rebels, who have also threatened to seize other territory held by the alliance west of the Euphrates river.
Only intervention by Washington has prevented Turkish troops from seizing the hard-won town of Manbij from the SDF.
Ankara views the Kurdish-led alliance as a terrorist group because of its links to the Kurdistan Workers’ Party (PKK), an outlawed rebel group that has been fighting Turkish troops since 1984.
Damascus too views Kurdish aspirations with suspicion and in late May President Bashar al-Assadthreatened to resort to force if necessary to prevent SDF-held areas breaking away.