A shroud of black smoke covered the Islamic State group's last redoubt in eastern Syria on Monday as US-backed forces battled holdout jihadists after a night of shelling and heavy air strikes.

Even as it fought IS, the Kurdish-led Syrian Democratic Forces also came under threat from Damascus, which has sworn to retake the third of the country the SDF controls.

The SDF has been closing in on IS fighters holed up in a small sliver of territory in the eastern village of Baghouz since January.

A cluster of rudimentary tents and vehicles is all that remains of the once-sprawling "caliphate" declared across large swaths of Syria and neighbouring Iraq in 2014.

Tens of thousands of men, women and children have poured out of the small farming village in recent weeks, slowing down an SDF offensive aimed at crushing the last vestige of the jihadist proto-state.

Backed by air strikes by the US-led coalition, the SDF pummelled the IS pocket with shelling on Sunday night, pushing deeper into the jihadist encampment.

Ground battles and artillery attacks continued on Monday as the Kurdish-led force worked to consolidate its most recent gains, SDF spokesman Adnan Afrin said.

"Clashes are ongoing between the SDF and IS" as the Kurdish-led forces secured positions it had seized inside the camp, he said.

On a hilltop overlooking the bombed-out bastion earlier, an AFP correspondent saw US-backed fighters training their guns on the camp.

"There, over there! Near the tree next to the bridge," a combattant shouted out, prompting another to unleash a torrent of machinegun fire in that direction.

Men -- believed to be jihadists -- could be seen shuffling inside the redoubt, beneath plumes of dark smoke that obscured most of the encampment.

- Kurdish areas to be 'liberated' -

Crouching behind rocks, SDF fighters opened fire at the presumed IS fighters that appeared near the banks of the Euphrates River.

"The SDF ground offensive has been very effective," coalition spokesman Sean Ryan said.

The SDF said on Sunday night that its forces had captured positions inside the camp.

Syria's minority Kurds have largely stayed out of Syria's eight-year civil war, instead carving out a de-facto autonomous region in the northeast of the country.

The Kurdish-led SDF now controls some 30 percent of the nation's territory, including areas from which it has expelled IS.

Syrian Defence Minister Ali Abdullah Ayoub on Monday said his government would recapture territory controlled by the SDF in the same way it "liberated" other parts of the country.

"The only card that remains in the hands of the Americans and their allies is the SDF," he said.

"The Syrian government will deal with this issue in one of two ways: a reconciliation agreement or liberating the territory they control by force," he said.

A shock announcement by President Donald Trump of a US troop pullout sent the Kurds scrambling to mend ties with Damascus to protect them from a feared Turkish offensive, but ongoing talks have yet to yield any results.

Eight years in to a conflict that has killed more than 370,000 people and displaced millions, President Bashar al-Assad's forces are in control of almost two-thirds of the country.

But the northeastern swathe held by the SDF, as well as the jihadist-held northwestern region of Idlib, remain beyond its control.

- Exodus -

It remains unclear exactly how many people remain inside the last IS pocket, but SDF spokesman Kino Gabriel on Sunday said those quitting the area put the number at up to 5,000 people.

More than 66,000 people, mostly civilians, have quit the last IS redoubt since January 9, according to the SDF.

They include 37,000 civilians, 5,000 jihadists and around 24,000 of their relatives.

An additional 520 IS fighters have been captured in SDF operations.

The huge numbers have flummoxed Kurdish forces, who are struggling to accomodate jihadists in Kurdish-run detention centres further north.

The exodus of civilians and relatives of fighters has also sparked a humanitarian crisis in Kurdish-run camps for the displaced.

The biggest of them is now struggling to host 70,000 people, including at least 25,000 school-aged children, according to the International Rescue Committee.

More than 123 people -- overwhelmingly under-fives -- have died on the way or shortly after arriving at the main camp of Al-Hol, the aid group said.

While SDF taking Baghouz would mark the end of the IS "caliphate", the jihadists still retain a presence in eastern Syria's vast Badia desert and have sleeper cells in Idlib.