NEAR BAGHOUZ (DNA) – Exhausted families trudged out of the Islamic State group s last bastion in eastern Syria Tuesday, as Kurdish-led forces boxed holdout jihadists into an ever-shrinking pocket.

Hundreds fled at night but hundreds more during the day as plumes of grey smoke billowed into the sky over Baghouz, where diehard IS fighters are making their last stand.

The extremist group declared a cross-border “caliphate” in Syria and Iraq in 2014, but various military campaigns have chipped it down to a fragment on the Iraqi border.

After a pause of more than a week to allow out civilians, the Syrian Democratic Forces (SDF) declared a last push to retake the pocket from the extremists on Saturday.

Aided by the warplanes and artillery of a US-led coalition, the Kurdish-led alliance has pressed into a patch of less than four square kilometres (one square mile).

SDF spokesman Mustefa Bali said 600 civilians fled the combat zone at night and the Syrian Observatory for Human Rights said another 350 made it out during the day.

The SDF have set up a pair of sand berms on a scrubby plateau overlooking Baghouz.

Most of the neighbourhoods visible along the hazy horizon are under their control, but the southernmost parts of the town — from which sounds of a firefight can be heard — are still held by IS.

Suddenly, black dots appeared on the dirt road that snakes across the plain from the ruins of the little town.

The SDF watched them warily at first, but as the group of about 25 people got closer, members of the Free Burma Rangers volunteer medical group scrambled down the hill to meet them.

There are no other NGOs or UN agencies at the site.

Half a dozen among the new arrivals were adult men. The rest were young children with dirty hair and women panting heavily after their odyssey out of Baghouz.

About half of them were Ukrainian or Russian women and their children, while most of the others were Syrian.

A 34-year-old woman from Crimea tore pieces of bread to give her three children. She identified herself as Umm Khaled and said she came to Syria five years ago after divorcing her Tatar husband.

Once there, she married an Azeri IS member and had two other children. “They are all fatherless now,” she told in broken Arabic, her voice shaking.

Coalition spokesperson Sean Ryan said US-backed forces were facing a fierce fightback.

“The progress is slow and methodical as the enemy is fully entrenched and IS fighters continue to conduct counter attacks,” he said.

“The coalition continues to strike at IS targets whenever available.”

On Monday, the Observatory said a coalition air strike killed 16 civilians.

An Italian journalist was also wounded as he covered the clashes and evacuated for treatment, a colleague said on Twitter.

The SDF launched the battle to expel IS from the eastern province of Deir Ezzor in September, slowly tightening the noose around the jihadists and their families since December.

In the past two months, more than 37,000 people, mostly wives and children of jihadist fighters, have fled into SDF-held areas, the Observatory says.

That figure includes some 3,400 suspected jihadists detained by the SDF, according to the Britain-based monitor.

At a gathering point for new arrivals, dozens of men knelt on the ground.

Iraqi and Syrian women and children prepared to make the long journey north to a Kurdish-held camp for the displaced, after spending the night in tents.