AL-OMAR OILFIELD (Syria) • Terrorists from the Islamic State in Iraq and Syria (ISIS) using tunnels and suicide bombers were mounting a desperate defence yesterday of the last square kilometre of their self-proclaimed "caliphate" in eastern Syria.

This came as Kurdish-led forces closed in on the small town of Baghouz, where ISIS fighters and their relatives were hunkered down, and met hundreds of famished and dishevelled people turning themselves in.

"The fighting is fierce," said Mr Adnan Afrin, a spokesman for the Syrian Democratic Forces (SDF), the Kurdish-Arab outfit that has been spearheading the campaign against ISIS with backing from a US-led coalition.

"There is significant resistance," he said at Al-Omar oilfield, the main staging base for the SDF's offensive against the very last shred of the original ISIS "caliphate".

The few hundred fighters of various nationalities holding out in their last bastion by the Iraqi border have launched bruising counter-attacks in recent days, Mr Afrin said.

The Islamists are clinging to about one square kilometre in the town's built-up area, as well as to an adjacent camp, where a number of civilians are believed to be gathered.

Mr Afrin said it was impossible to provide accurate figures, but he estimated the total number of fighters - men and women - at 1,000. "There are many tunnels in Baghouz now. This is why the operation is dragging on. There are many suicide bombers attacking our positions, with explosives-laden cars and motorbikes."

He also said two such suicide attacks were carried out by women on Tuesday, but he would not provide any figures on casualties among SDF ranks.

Meanwhile, hundreds of people are continuing to trickle out of the last ISIS redoubt daily, trudging up a dirt road to a collection point where SDF fighters and volunteers provide first aid and carry out a first screening. Many of those who fled had had to sleep outside in the cold to reach that point, where a lucky few get tents while the rest were spread out on cheap blankets.

"This is the second night we sleep outside. There was so much bombing in Baghouz that it was safer for us to sleep in the open," said Fatima, an Iraqi woman from Baghdad who fled Baghouz with her four children, all under 15.

The US-led coalition is carrying out air strikes on the area, while its forces are also present on the ground, sifting through the displaced for wanted extremists.

Mr Afrin said SDF forces tuning their walkie-talkies on the militant's frequencies "can hear them speak in Arabic, but also in Turkish, French and English".

Once the adult men have been separated from their families, foreign and SDF officers thumb through pictures on smartphones to ask new arrivals about wanted ISIS leaders.

The terrorist group's elusive Iraqi-born supremo, Abu Bakr al-Baghdadi, is not believed to be among the last ISIS leaders holed up in Baghouz. Several known Islamist figures have emerged from the dregs of the "caliphate" in recent days, however, including German Martin Lemke and Frenchman Quentin Le Brun.

A rift appears to have grown between foreign members of ISIS - who have nowhere to hide - and local fighters, who are attempting to blend back into the population as the organisation goes underground again.

An official declaration of victory against ISIS is expected in the coming days, a move of mostly symbolic value that will go down as the death certificate of the "caliphate", even as the terror organisation remains a threat.

AGENCE FRANCE-PRESSE