NEAR BAGHOUZ, Syria (Reuters) - Dozens of relatives of foreign fighters including Iraqis, Turks, and Russians fled Islamic State’s last bastion in eastern Syria on Tuesday as the jihadists lost ground to U.S.-backed forces.

A field commander with the Kurdish-led forces, which are pushing further into the besieged pocket, said mostly foreign militants were making their last stand.

The Syrian Democratic Forces (SDF), which holds about a quarter of the country, has mounted an attack to seize the enclave with the help of U.S. air strikes. Many hundreds of civilians streamed out in the past two days alone.

The SDF made “slow and methodical” progress in the battle near the Iraqi border, according to the U.S.-led coalition backing it.

Jets roared in the sky and the sound of an explosion rang out from Baghouz, the last village in the area that is partly in Islamic State hands, a Reuters witness said.

Around 300 civilians who fled on Tuesday were transferred in trucks to a camp in the northeast. They appeared exhausted or hungry, and some of the children were barefoot.

Several people identified themselves as Iraqi, Turkish, Ukranian or Russian.

A fleet of 15 vehicles carrying U.S. forces headed along a dirt road towards the frontlines.

At the edge of Baghouz, civilians who had escaped stood in line for questioning by U.S. and SDF forces who were apparently trying to find wanted militants.

The SDF believes 400 to 600 militants remain holed up in the enclave, including many hardened foreigners and some emirs. Its spokesman said last month that most of the civilians still there were the wives and children of the militants.

“We are seeing fierce resistance from the Daesh fighters,” SDF field commander Adnan Afrin told Reuters on the outskirts of Baghouz.

FILE PHOTO: Members of Syrian Democratic Forces (SDF) stand near a pick up truck near Baghouz, Deir Al Zor province, Syria February 11, 2019. REUTERS/ Rodi Said/File Photo

“Most are foreigners, Iraqis, Europeans. There are a lot of Turks. We can hear them on the walky-talkies.” He said the jihadists now held only one square km (0.4 square miles) of the village.

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CIVILIANS FLEEING

“The bombing was unimaginable, we ran from one place to the other,” said Hala Hassan, 29, a woman from Syria’s Deir al-Zor who escaped with her five children.

She said “fighters from all nationalities” were in the enclave. “There was no food. We ate grass from the ground like sheep...Daesh had blocked the roads and smugglers wanted thousands of dollars.”

Intisar Abdel-Hafez, 30, an Iraqi woman who fled with her children, said her husband was a teacher who had stayed in Baghouz with his elderly mother.

She said her husband had moved the family across the border into Syria nearly three years ago and she did not leave the enclave earlier because of the shelling.

Coalition spokesman Colonel Sean Ryan said it was too early to say when the offensive would end. “ISIS fighters continue to conduct counter attacks,” he said by email on Tuesday.

Air strikes, crucial to SDF gains, have levelled entire districts in the battle against Islamic State, though the coalition says it takes care to avoid hitting civilians.

A UK-based war monitor and Syrian state media said strikes had killed 16 civilians overnight in a camp in Baghouz. Ryan said the coalition was looking into the report.

Syria’s foreign ministry urged the United Nations “to stop these crimes...and end the aggressive, illegitimate presence of American and other foreign forces.”

Islamic State redrew the regional map in 2014 when it declared a caliphate across swathes of Syria and Iraq. But the jihadists steadily lost to various offensives and their main prizes - Syria’s Raqqa city and Iraq’s Mosul - fell in 2017.

The SDF, which the Kurdish YPG militia spearheads, advanced into Deir al-Zor after capturing Raqqa. Its operations have focused on territory east of the Euphrates River.

To the west of the river, in territory otherwise under the control of the Syrian army and its allies, Islamic State retains a foothold.

U.S. President Donald Trump said in December he would pull all 2,000 American troops out of Syria, announcing the battle against Islamic State almost over.

But Islamic State is still widely seen as a threat. A top U.S. general said last week the militants would be an enduring menace after the withdrawal, as they retained leaders, fighters, and resources that would fuel further insurgency.