An Iraqi commander said his troops are within 900 yards of the main government complex in the northern city of Mosul, the capture of which would mark a symbolic victory against the Islamic State.

Maj. Gen Thamir al-Hussaini of Iraq’s elite rapid-response units said his forces were advancing along the Tigris River after retaking one of the city’s five damaged bridges. He said the capture of the bridge could shorten supply lines and allow civilians in western Mosul, where heavy fighting is underway, to flee to the government-controlled eastern half of the city.

“In the coming day, we will clear the government buildings,” he told reporters in Abu Saif, a village outside Mosul.

Inside the city, residents described Iraqi forces’ hold on the area as much more tenuous.

Within a few hundred yards of the bridge, makeshift roadblocks set up to prevent car bombs were still in place, preventing civilian and military traffic.

“None of the main road has been liberated yet,” said Muhammad Salah, a resident of a recently retaken neighborhood nearby.

Cpl. Hussein Ishaq, a member of the rapid-response units, described the battle for the neighborhood as “simple,” saying that Islamic State defenses were light and that his forces cleared the district in a single day.

Residents said, however, that Iraqi forces pushed into the area only after days of heavy airstrikes and artillery fire.

“Honestly, it was a very fierce fight,” Salah said.

The United Nations’ migration agency, meanwhile, reported a surge in the number of fleeing civilians, saying that more than 10,000 men, women and children have been displaced since the operation to retake western Mosul began Feb. 19. The International Organization for Migration (IOM) cited Iraqi government figures.

The IOM, citing accounts from those who have fled, said the streets are littered with the bodies of slain militants as well as civilians. It said militants have raided the shops, warehouses and homes of those who have fled as they stockpile supplies.

More than 220,000 people have fled since U.S.-backed Iraqi forces launched an offensive to retake Mosul in October, according to the IOM. Of those, more than 175,000 remain displaced.

The western half of Mosul is the last significant urban area held by the Islamic State in the country. The city fell to the Islamic State in 2014.