BAGHDAD: More than 4,000 people have fled the Islamic State-held city of Fallujah in Iraq after government forces retook a key road to the IS stronghold over the weekend, an aid group said on Monday. Along with roadside bombs planted by the militants, an estimated number of 50,000 civilians who remain trapped inside Fallujah, located about 40 miles (65 kilometers) west of Baghdad, have slowed down the Iraqi forces' operation to recapture the city. Fallujah has been under IS control for over two years the last major city in western Iraq still held by the extremist group. The militants have threatened anyone who attempts to flee with death and last week they reportedly shot at a group of civilians attempting to flee across the Euphrates River. The Norwegian Refugee Council, which works with refugees and internally displaced Iraqis, said the 4,000 who fled since Saturday bring the total number of residents who escaped Fallujah since the Iraqi offensive started in late May to 27,580. Thousands more are expected to take the risky journey in the coming hours, NRC said, adding that some refugees reported IS militants were demanding 150,000 Iraqi Dinars, or around $130, from each person to let them leave. The aid group warned that humanitarian resources are running low and called for at least $10 million for a six months' supply of water, food and basic necessities. 'Thousands of others remain trapped inside and the most vulnerable will need urgent assistance,' said NRC Country Director in Iraq Nasr Muflahi. On Sunday, the Iraqi command announced that key areas to the west of Fallujah have been taken and that Iraqi forces pushed deeper into the city from its southern edges. U.S.-trained Iraqi counterterrorism forces, wary of coming street battles in the city, are already facing fierce resistance on the outskirts from well-entrenched militants.