US-backed forces pressed the battle to expel diehard jihadists from the last pocket of land under their control in eastern Syria on Tuesday after hundreds fled the holdout overnight. The extremist group declared a cross-border "caliphate" in Syria and Iraq in 2014, but various military campaigns have chipped it down to a fragment on the Iraqi border. After a pause of more than a week to allow out civilians, the Syrian Democratic Forces (SDF) declared the last push to retake the "Baghouz pocket" from the extremists on Saturday. Aided by the warplanes and artillery of a US-led coalition, the Kurdish-led alliance has made way into a patch of four square kilometres (one square mile). SDF spokesman Mustafa Bali said heavy clashes were ongoing on Tuesday after hundreds fled the battle zone overnight. "A group of 600 civilians escaped from Baghouz at one in the morning and they are being searched now," he said. The Syrian Observatory for Human Rights said the new arrivals included women and children from France and Germany. "Most of those who got out are foreigners," Observatory chief Rami Abdel Rahman said. Coalition spokesperson Sean Ryan said US-backed forces were facing a fierce fightback. "The progress is slow and methodical as the enemy is fully entrenched and IS fighters continue to conduct counter-attacks," he said. "The coalition continues to strike at IS targets whenever available." The SDF launched the battle to expel IS from the eastern province of Deir Ezzor in September, slowly tightening the noose around the jihadists and their families since December. French women In the past two months, more than 37,000 people, mostly wives and children of jihadist fighters, have fled into SDF-held areas, the Observatory says. That figure includes some 3,400 suspected jihadists detained by the SDF, according to the Britain-based monitor, which relies on sources inside Syria for its information. On Monday, AFP saw dozens of new arrivals at an SDF-held screening location. Dozens of coalition and SDF fighters were stationed at a screening point for new arrivals from IS areas. Coalition forces stood over about 20 men who were crouching on the ground. Two French women told AFP they paid smugglers to take them out of the battered IS-held holdout, but Iraqi jihadists had prevented other foreigners from leaving. "They said only the Syrians and Iraqis can be smuggled out," said one of the women, who gave her first name as Christelle, from the city of Bordeaux. Bali, the SDF spokesman, said on Saturday that up to 600 jihadists could remain inside the pocket. But the group`s elusive leader Abu Bakr al-Baghdadi who proclaimed the "caliphate" in 2014 was likely not there, he said. At the height of their proto-state, Baghdadi`s followers implemented their brutal implementation of Islamic law in an area the size of the United Kingdom. But various offensives, including by the US-backed SDF and Russia-backed regime forces, have taken back all but a morsel of that territory near the village of Baghouz. `Clearing operations` Once the "caliphate" is declared over, the fight will continue to eliminate IS sleeper cells, the SDF and their allies have said. "After Baghouz, clearing operations will have to take place as well," Ryan said. "IS has purposely left IEDs (improvised explosive devices) behind to intentionally kill innocent civilians." The jihadist group, also known as ISIS, retains a presence in Syria`s vast Badia desert and has continued to claim deadly attacks in SDF-held areas. US President Donald Trump on Monday said that the coalition may declare victory over IS in the region in the coming days. "Our brave warriors have liberated virtually 100 per cent of ISIS (territory) in Iraq and Syria," he said. "Soon it will be announced, soon, maybe over the next week, maybe less," he told a rally in the US city of El Paso. Trump shocked Washington`s allies in December by announcing a pullout of all 2,000 US troops from war-torn Syria. The decision has left Syria`s Kurds scrambling for protection from Damascus against a long-threatened attack by neighbouring Turkey. After decades of marginalisation, the Kurds have largely stayed out of the eight-year civil war, instead of setting up their own semi-autonomous institutions in northeast Syria. Syria`s war has killed more than 360,000 people and displaced millions since starting in 2011 with the brutal repression of anti-government protests.