The warning by the US-backed Syrian Democratic Forces (SDF) came as European nations reacted coolly to a USA call to repatriate their nationals from Syria, which Germany said would be "extremely difficult". Once in control of about a third of Syria and Iraq, they now are down to what SDF officials describe as a small tented village atop a network of tunnels and caves.
The capture of Baghouz and nearby areas would mark the end of a devastating four-year global campaign to end the extremist group's hold on territory in Syria and Iraq, their so-called "caliphate" that at the height of the militant group's power in 2014 controlled almost a third of both Iraq and Syria.
The group declared a "caliphate" across large swathes of Syria and neighboring Iraq in 2014, which at its height spanned an area the size of United Kingdom. Occasional airstrikes and artillery rounds by the US -led coalition supporting the SDF, meant to clear land mines for the advance, could be seen in the distance.
The SDF are on the brink of defeating IS in Baghouz, where it estimates a few hundred Islamic State fighters and about 2,000 civilians are under siege.
The Syrian Observatory for Human Rights, a Britain-based war monitor, said the SDF have turned down the request.
Despite the SDF, the Kurdish-Arab outfit that has spearheaded the campaign against ISIS with backing from a US-led coalition, holding the military capacity and advantage to enter the town, they are maintaining positions on the outskirts in fear of an offensive pushing ISIS to take local civilians as human shields.
The SDF attacking Islamic State have an obligation under worldwide law to take all precautions to protect civilians who are mixed in with the foreign fighters, he said.
Hungarian Foreign Minister Peter Szijjarto said the issue is "one of the greatest challenges ahead of us for the upcoming months".
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The Kurdish-led SDF fighters are busy clearing improvised explosives from the area while staying on the lookout for any IS suicide bombers.
"We must be able to ensure that prosecution is possible", she said.
Security experts have warned that convicted terrorists will walk free from European prisons by the dozens over the next two years, many of them jihadis who trained or fought in Syria and Iraq but never faced serious charges due to insufficient evidence.
Trump tweeted: "The United States is asking Britain, France, Germany and other European allies to take back over 800 Isis fighters that we captured in Syria and put them on trial".
The general overseeing USA forces in the Middle East flew into Iraq on Sunday for talks with US and Iraqi officials expected to focus on ensuring that Islamic State can not stage a resurgence after USA troops withdraw from neighbouring Syria.
Thousands of ISIS fighters and their families have emerged from the last bastion held by the group in the past few months.
He then reiterated his claim that "The Caliphate is ready to fall". "They're not talking to each other as much", he added. We are pulling back after 100% Caliphate victory!'
The message comes as USA -backed Syrian forces are poised to seize control of ISIS's last stronghold, the town of Baghuz, which is on the Syrian side of the border with Iraq.