Iraqi troops battled Daesh fighters for control of a bridge over the River Tigris in Mosul on Tuesday as civilians streamed out of recaptured western neighborhoods, cold, wet and hungry but relieved to be free of the militants' grip. Progress by Interior Ministry Rapid Response units had been slowed by rain on Monday but heavy fighting resumed on Tuesday, with the Iron Bridge the prize at stake. Government forces also pushed into areas of western Mosul, Daesh's last redoubt in the city that has been the de facto capital of their self-declared caliphate. The troops had advanced to within 100m (330 feet) of the bridge but were slowed by sniper fire from gunmen positioned in high buildings, a Rapid Response media officer told Reuters. "Our forces managed to resume advancing inside the old city center after weather improved and succeeded in retaking the Korneesh street which runs by the riverside. It's very key for our forces to secure the riverside and prevent Daesh militants from turning around our advancing forces," he said. They expected to gain control of the Iron Bridge and the nearby area by the end of the day. "Seizing the bridge will help further tighten the noose around Daesh fighters entrenched inside the old city," he said. The bridge connects Mosul's Old City with the eastern side of the city. Capturing it would mean Iraqi forces control three of the five bridges in Mosul that span the Tigris, all of which have been damaged by the militants and US-led air strikes. The southernmost two have already been retaken by Iraqi forces. Since starting the offensive in October, Iraqi forces with US-led coalition support have retaken eastern Mosul and about 30 percent of the west from the militants, who are outnumbered but fiercely defending their last stronghold in Iraq. The boom of shelling and heavy machinegun fire could be heard from the center of Mosul and helicopter gunships strafed the ground from above on Tuesday morning. Amid the combat, a steady stream of refugees trudged out of the western districts, carrying suitcases, bottles of water and other possessions. Some pushed children and sick elderly relatives in handcarts and wheelbarrows. Soldiers packed them into trucks on the Mosul-Baghdad highway to be taken to processing areas. Most left in the dark early morning hours or after the army recaptured their neighborhoods. Food had been scarce, they said. "We fled at 5 a.m. (0200 GMT) after the army had arrived. There has been a lot of shelling by Daesh," said Hamid Hadi, a teacher. "Mostly we've been eating water mixed with tomatoes." Ashraf Ali, a nurse who escaped with his wife and two children, said mortar rounds were falling as they fled. They took advantage of the army retaking their district to get out. "Daesh wanted us to move to their areas but we escaped when the army arrived," he said. As many as 600,000 civilians are caught with the militants inside Mosul, which Iraqi forces have effectively sealed off from the remaining territory that Daesh controls in Iraq and Syria. The Iraqi forces include army, special forces, Kurdish peshmerga and Shiite militias. More than 200,000 Mosul residents have been displaced since the start of the campaign in October, of which more than 65,000 fled their homes in the past two weeks alone, according to the International Organization for Migration. "Whenever we advance there are more people coming out," said one Iraq officer directing refugee transport. "There are more people on this side of the city and people are trying to leave because there is no food and no supplies in their area." Residents also fled from the Wadi Hajjar district on Monday carrying bags and belongings through the muddy streets to areas controlled by the army before being transported out by truck. "It was a nightmare and we are finally done with it. It cannot be described. There is no water and there is no food and nothing," said resident Ghanem Mohamed. Federal police forces have also been fighting pockets of militants in areas close to the Iron Bridge. At the weekend, they entered the Bab Al-Tob area of the Old City, where fighting is expected to be toughest because of its narrow alleyways. The military said on Monday that elite Counter Terrorism Service troops, known as CTS, managed to retake the Al-Nafut district of west Mosul. Losing Mosul would be a major strike against Daesh. It is by far the largest city the militants have held since their leader Abu Bakr Al-Baghdadi proclaimed himself leader of a self-styled "caliphate" spanning Iraq and Syria from a mosque in Mosul in the summer of 2014.