US-backed fighters have transported civilians from the last speck of Islamic State’s dying “caliphate” in Syria, as they press on with the battle to defeat the jihadist group.

More than four years after Isis overran large parts of Syria and neighbouring Iraq to declare a caliphate, it has lost all but a tiny patch in the village of Baghouz near the Iraqi border.

More than 40 trucks carrying men, women and children left the enclave on Friday, according to AFP reporters at a position of the Syrian Democratic Forces (SDF) outside the village.

Most were women and children, their clothes caked in dust, but the passengers also included men with their faces wrapped in chequered scarves. Women clung to the railings of the trucks as they departed in the second such large-scale evacuation in three days.

On the back of one of the trucks, three men covered their faces with their hands, apparently not wanting to be caught on camera. One woman raised the index finger of her right hand in an Islamist gesture.

Asked what the situation was like inside Baghouz, a young man replied: “Not good.”

An SDF spokesman, Adnan Afrin, said more than 2,000 people were estimated to still be inside the pocket of territory, and more trucks were expected to bring them out. Once the evacuations have ended, the SDF would expel the last jihadists from the less than half a square kilometre (a fifth of a square mile) they still hold, he said.

“When the civilians leave, we will see how many civilians and IS fighters remain inside and what they want to do,” he said. “They will be faced with a choice: war or surrender.”

Men, women and children ride in the back of a truck leaving the village of Baghouz. Photograph: Felipe Dana/AP

Earlier on Friday, another SDF spokesman, Mustafa Bali, said he hoped civilian evacuations could be completed by Saturday.

The SDF evacuated 3,000 people on Wednesday – mostly women and children – but the trucks that left on Thursday were almost empty.

Bali said screening had determined that most of those evacuated on Wednesday were foreigners. “The majority are Iraqi and from countries of the former Soviet Union, but there are also Europeans among them,” he said.

David Eubank, the leader of the Free Burma Rangers volunteer aid group, said they included many French women, as well as others from Australia, Austria, Germany and Russia, and one woman from Britain.

Human Rights Watch, a New York-based watchdog, urged the SDF and the US-led coalition to make protecting civilians a priority.

“Just because they may be families of Isis members or sympathised with them does not take away their protected status,” the watchdog’s Nadim Houry said.

Beyond Baghouz, Isis retains a presence in the vast Syrian desert and sleeper cells elsewhere, and continues to claim deadly attacks inside SDF-held territory. On Thursday, the group detonated a car bomb that killed 20 people near the Omar oil field, the main base for the SDF operation in Baghouz.

The battle for the village is now the only live front in Syria’s complex war, which has killed 360,000 people and displaced millions since 2011. Any SDF victory in Baghouz would accelerate an expected withdrawal of US troops from Syria announced in December by the US president, Donald Trump.

Kurdish forces, who have spearheaded the US-backed fight against Isis in Syria, have expressed fear that a full pullout would leave them exposed to a long-threatened attack by neighbouring Turkey.

But Washington said on Thursday the US military would keep some troops in Syria after the withdrawal. “A small peacekeeping group of about 200 will remain in Syria for a period of time,” the White House spokeswoman, Sarah Sanders, said.

At the height of its rule, Isis imposed its brutal ideology on an area roughly the size of the UK, attracting thousands of supporters from abroad. But some of those foreigners have been killed, while the SDF holds hundreds more.

Syria’s Kurds have long requested that the Isis members’ home countries take them back, but foreign governments have been reluctant.

On Thursday, the father of Hoda Muthana, 24, who joined Isis in Syria, sued to bring her home after the Trump administration declared she was not a US citizen.

The London teenager Shamima Begum, meanwhile, faces being left stateless after Britain said it would revoke her citizenship after she joined Isis aged 15, and authorities in Bangladesh, where her parents were born, said the country would not take in the now 19-year-old.