Clambering up dirt berms, clutching babies and blankets, the latest refugees of the Islamic State could well be the last.

Inside the nearby enclave they fled are perhaps no more than 500 people – nearly all of them fighters who are refusing to leave a two square kilometre corner of eastern Syria that is all that remains of the group’s so-called caliphate.

US-backed Syrian forces launch attack on final Isis stronghold Read more

The women and children who escaped the eastern Syrian town of Baghuz on Tuesday were not supposed to be there. Weeks of bombing and an exodus that had largely accounted for the pre-war population of 9,000 had given the besieging Kurdish-led forces a clear run at the holdouts in the ruins – or so they thought.

After three days of intensive bombardment, more people emerged than the attackers had thought possible, slowly making their way to collection points adjoining the battlefield. They included women from France, Russia and Tajikistan, as well as families from Iraq and nearby Syrian towns and cities.

Facebook Twitter Pinterest Women and children arriving at a collection point for Isis families fleeing the battleground of Baghuz in eastern Syria. Photograph: Achilleas Zavallis/The Guardian

As the utopian promise of Isis has become a bloody, shrinking dystopia, Baghuz has been a collection point for fighters and their families from across the lands the group once controlled.

“There are more women and children of Isis left inside than we expected before starting the operation on Saturday,” said Adnan Afrini, a commander from the Kurdish unit, known as the SDF. “We are receiving hundreds of Isis families and their children every day.”

Crammed into a forsaken enclave on the banks of the Euphrates river, the remnants of Isis and their supporters have nowhere to run. And those that have not left by now are unlikely to do so in the coming week, in which Kurdish forces expect Baghuz to be cleared of the extremists.

“We are facing severe fighting because the area that we are surrounding is very small,” said Afrini. “It is very dense with fighters, and they are among their most extreme and experienced soldiers. They use suicide bombers in their counterattacks and tunnels. There is no sign of surrender. The fighters left inside are the most extremist and ideologically driven militants.”

Hamada Hussein, 50, from Qaim, was one of the new exiles. On a field littered with food rations and water bottles, she said she had walked for four hours to safety, and would now accept whatever fate had in store for her. “There is nothing left inside Baghuz,” she said. “We could only eat once a day. There are some women and children left inside who can’t get out because of clashes. The town is all destroyed, and bullets are flying through the sky like rain.”

Like many others standing in the field, Hussein said she was from outside the town, but had fled to Baghuz as war waged all around her.

Abu Ahmad al Rawi, 35, from Rawa, in Iraq was another. “We didn’t have any chance of getting out until now,” he said. “We were in Keshma before moving to Baghuz, and the war got here too.

“I moved to Syria after the advance of the Shia militias to Rawa. I didn’t have any other choice. I don’t know what will happen after this but I knew that was the only way to stay alive.”

Facebook Twitter Pinterest As Isis families flee their former stronghold, Kurdish forces say they have taken in over 1,000 people in two days. Photograph: Achilleas Zavallis/Achilleas Zavallis for The Guardian

Salih Omar, a member of a local civic council, said more than 1,000 Isis family members had been received by Kurdish forces in the past two days and would be taken to nearby refugee camps. They are thought to include more foreigners than Iraqis, adding to some 10,000 non-Syrians being sheltered by local authorities in the Kurdish north.

Four days into the final stages of a fight widely billed as the last conventional battle in the four-and-a-half year war against Isis, there is little sign of a deal to allow the remaining diehards to flee to the deserts – their only possible escape route. Such an arrangement brought the fight for the city of Raqqa to a close in late 2017, with fighters and their families bussed to the central Syrian deserts, from where many disappeared.

“It was an SDF initiative and a Faustian pact,” said Shiraz Maher, director of the the International Centre for the Study of Radicalisation at King’s College London. “They said to Isis, we’re surrounding you. We’re going to kill you all. Isis appreciate the value of a strategic retreat. It suited both sides for that deal at the time. It gave them a headline victory, and Isis the way to fight another day.”

Now, with the endgame looming, there are no signs that a similar deal will be offered in Baghuz.

Isis is known to hold foreign hostages in or near Baghuz – including the British hostage John Cantlie – whom it plans to use as bargaining chips.

As the war winds down, recovering the hostages is a high priority for the SDF. So too is marking the victory as soon as possible – the Kurds are already constructing a celebratory stage on one of their main bases.

“I’m confident that within days we’ll celebrate victory and the end of the so-called caliphate,” said Afrini.

• This article was amended on 14 February 2019. “Clamouring” in the introduction was changed to “clambering”.