Islamic State faced imminent defeat in its final enclave as hundreds of jihadist fighters and their families surrendered and the US-backed Syrian Democratic Forces said the battle was as good as over.

The besieged enclave of Baghouz is the last shred of territory held by the jihadists, who have been driven from roughly one third of Iraq and Syria over the past four years.

A Reuters journalist in Baghouz saw hundreds of people surrendering to the SDF, which launched its final attack to capture Baghouz on Sunday, backed by US-led international coalition air strikes and after weeks of siege.

SDF official Mustafa Bali said a large group of Islamic State fighters and their families had surrendered en masse.

“Once our forces confirm that everyone who wants to surrender has done so … the clashes will resume,” he said. The jihadists’ defeat was very near, he said.

The Baghouz enclave was pounded overnight with barrages of rockets and fires raged inside, but the situation was calm on Tuesday morning.

“The operation is over or as good as over, but requires little more time to be completed practically on the ground,” SDF spokesperson Kino Gabriel told al-Hadath TV.

The SDF has been laying siege to Baghouz for weeks, but repeatedly postponed its final assault to allow the evacuation of thousands of civilians, many of them wives and children of Islamic State fighters. It finally resumed the attack on Sunday, backed by coalition air strikes.

Gabriel said 25 Islamic State fighters had been confirmed killed so far in clashes, in addition to an unknown number of militants killed by air strikes. Another SDF official earlier said 38 jihadists had been confirmed killed.

The SDF, which is spearheaded by the Kurdish YPG militia, has been advancing slowly into Baghouz to minimise its losses from sniper fire and landmines. Three SDF fighters have been killed, Bali said on Twitter.

Islamic State’s defences include extensive tunnels. The militant group’s most hardened foreign fighters are holed up inside the enclave, the SDF has said.

However, the US does not believe any senior Islamic State leaders are in Baghouz, assessing they have gone elsewhere as part of the group’s shift towards guerrilla tactics, a US defence official has aid.

While Baghouz is the last populated territory of what was once the group’s self-proclaimed “caliphate,” fighters still operate in remote areas elsewhere. It is widely assessed that they will continue to represent a potent security threat.

The bulk of the people evacuated from the diminishing Islamic State territory have been transported to a camp for internally displaced people in al-Hol, in north-eastern Syria, where the United Nations says conditions are dire. The camp, designed to accommodate 20 000 people, is now sheltering more than 66 000.

The World Health Organisation said 106 people, mainly infants, have died since December on the journey toal-Hol, which takes at least six hours.

Many evacuees, particularly foreigners, still express obdurate support for Islamic State, posing a complex security, legal and moral challenge. Those issues were underscored on Friday with the death of the newborn son of Shamima Begum, a British woman who left to join Islamic State when she was a schoolgirl.