Syrian President Bashar al-Assad on Monday called US-backed Kurdish fighters "traitors" during a bitter exchange of insults with a force that controls more than a quarter of the country.

Kurdish groups in northern Syria have carved out self-governing autonomous regions since early on in the country's six-year civil war.

Last month, Kurdish authorities in northern Syria announced that phase two of regional elections will take place on 1 December.

The elections will culminate with the selection of an assembly in January that will serve as a parliament for a federal system of government in the Kurdish-controlled territories in Syria.

"When we talk about those referred to as 'the Kurds', they are in fact not just Kurds. All those who work for a foreign country, mainly those under American command... are traitors," Assad said on Monday.

"This is how we see these groups working for the Americans," he added.

Assad had criticised the semi-autonomous Kurds in the past, but his latest remarks, released by the presidency on social media, were more virulent than usual.

Both Damascus - backed by Russia - and the Kurds - backed by a US-led coalition - have fought the Islamic State group in recent months.

But their common enemy has been defeated across much of the country now, leaving the Kurdish-dominated SDF and regime forces in an uneasy face-off.

Some senior regime officials had in the past made overtures to the Kurds, suggesting some level of autonomy could eventually be discussed, but Assad's latest comments augur poorly for any future talks.

The SDF hit back at Assad later on Monday, accusing the Syrian regime president of opening the country's borders to "foreign terrorists".

"Bashar al-Assad and what's left of his regime are the last people with the right to talk of treachery," the Kurdish-dominated Syrian Democratic Forces said.

"It was the regime that flung the country's doors wide open to hordes of foreign terrorists from across the world."

The Kurdish minority accounts for an estimated 15 percent of Syria's population and the Kurdish People's Protection Units (YPG) control a large chunk of territory in the country.