The jihadists once ruled over millions in a swathe of Syria and Iraq, but they have since lost all that territory except for a riverside slither of land near the Iraqi border.

The US-backed Syrian Democratic Forces paused their months-old offensive against the shrinking holdout multiple times for thousands of dust-covered women, children and men to flee, including suspected jihadists.

After that human flow slowed to a trickle, the Kurdish-led SDF late Sunday warned remaining IS fighters that time was up for any surrenders and they were going in.

After a night of heavy bombardment that saw the SDF move forward and hundreds of people surrender, the front was relatively quiet on Monday afternoon.

Near the frontline earlier in the day, warplanes were heard rumbling overhead, and the sound of sporadic gunfire rang out from the jihadist encampment, AFP correspondents said.

SDF fighters sat on plastic chairs on the roof of an abandoned building, watching the camp hundreds of metres (yards) away, beyond fields dotted with palm trees.

"The clashes were heavy" overnight, SDF unit commander Aras Orkeish told AFP, with IS launching "suicide bombers" and "car bombs" at them.

"The operation slowed down after midnight," he said.

"Several hundred (people) gave themselves up and we paused to get them out," he added.

Special units carried out preliminary searches to weed out suspected jihadists, and operations would resume at night if their were no new surrenders, Orkeish said.

- Wounded fighter -

With its sirens screaming, an ambulance Monday hurtled across the ruins in the village of Baghouz.

A small pickup truck followed, a female SDF fighter in the back tending to two comrades lying under blankets, one with his leg bandaged.

The SDF launched the renewed assault on Sunday after no civilians were observed to remain in the riverside encampment.

By Monday morning, the SDF had seized several positions from the jihadists, an official with the US-backed forces said.

The warplanes of a US-led coalition and mortar fire overnight pounded weapons caches, and tank fire targeted IS positions, he and a spokesman said.

It was unclear how many people remained inside the pocket on the banks of the Euphrates, SDF spokesman Mustefa Bali said late Sunday.

"We expect there to be from 1,000 to 1,500 terrorists inside," he said.

"During the advance, if our forces notice the presence of civilians our special units... will do the necessary to bring them away from the clashes or even work to evacuate them," he said.

Since December, nearly 59,000 people have left the last IS redoubt, according to the Syrian Observatory for Human Rights, around a tenth of them suspected jihadist fighters.

The last IS fighters are clinging on to an area that includes a dismal camp of vehicles and cloth-covered trenches by the reedy banks of the Euphrates.

The SDF pushed into the IS encampment some 10 days ago, discovering spent ammunition, pots and pans lying between hastily-dug trenches and berms.

- Humanitarian crisis -

At the height of its brutal rule, IS controlled a stretch of land in Syria and Iraq the size of the United Kingdom.

The total capture of the Baghouz camp by the SDF would mark the end of the cross-border "caliphate" it proclaimed in 2014.

But beyond Baghouz, IS retains a presence in eastern Syria's vast Badia desert and sleeper cells in the northeast.

They have continued to claim deadly attacks in SDF-held territory in recent months, and the US military has warned of the need to maintain a "vigilant offensive".

The United States is expected to keep 200 "peace-keeping" troops in Syria after the end of the offensive, despite President Donald Trump's shock announcement in December that all 2,000 American soldiers would leave.

The exodus from Baghouz in recent months has sparked a humanitarian crisis, leaving aid organisations struggling to cope.

Those fleeing Baghouz have emerged exhausted and hungry after a prolonged siege.

Dozens of young children have died along the way or shortly after arriving at a Kurdish-run displacement camp in northeast Syria, according to the International Rescue Committee aid organisation.

Syria's Kurds hold hundreds of foreigners accused of fighting for IS as well as members of their families.

But their home countries have mostly been reluctant to take them back, with Britain stripping several women of their nationalities.

Morocco said it had repatriated from Syria on Sunday eight of its nationals suspected of belonging to IS.