US-backed forces have taken control of 70 percent of Manbij after rapid advances against areas controlled by the Islamic State of Iraq and the Levant (ISIL) in the key Syrian city near the Turkish border, a spokesperson for the group says.

Syria Democratic Forces (SDF), with the support of air strikes, have cornered rival armed groups, including ISIL, in the city's old quarter after seizing most of the eastern, western, and southern parts of the city, Sharfan Darwish of the SDF-allied Manbij Military Council told Reuters on Sunday.

SDF forces "have been increasingly besieging" and "encircling Manbij", Al Jazeera's Mohammed Jamjoom said earlier in the day, reporting from Turkey's Gaziantep.

"Even though there is a semblance of relief for those thousands of people who were able to leave those ISIL-dominated areas of the city, we must remember there are still thousands trapped inside areas that are still held by ISIL," Jamjoom reported.

"And there are a lot of fears about what coalition air strikes could bring with regards to civilian casualties in the days to come," he said.

"[The] relief is very much contrasted by these concerns about the mounting civilian death toll from coalition air strikes."

READ MORE: Barrel bombs in Syria

The Observatory reported on Sunday that at least 2,300 civilians fled the city in a 24-hour period.

The US-backed SDF, which includes a Kurdish armed group and Arab allies, launched its campaign to take Manbij, and drive ISIL from the Syrian-Turkish frontier, nearly two months ago with the backing of US special forces.

'Shooting almost constantly'

Syrian state media reported on Sunday that dozens of families, as well as some opposition fighters, have started using newly opened "humanitarian corridors" to leave rebel-held parts of Aleppo.

Yet conflicting reports from inside the besieged city suggested that the corridors are not yet in operation.

Sources in Aleppo told Al Jazeera that the corridors had not been opened, and civilians were still coming under fire.

READ MORE: What changes lie ahead after al-Nusra\'s al-Qaeda split?

"Everybody that we've spoken with, when it comes to opposition activists and residents in the rebel-held areas of Aleppo, have told us that these humanitarian corridors have not been opened," Al Jazeera's Jamjoom said.

"Not only have they not been opened, but they say in several of the areas ... in fact there is fighting still going on, and there are regime snipers as well that are shooting almost constantly."

An estimated 320,000 people are under government siege in Aleppo, facing acute food and medicine shortages.

The Syrian conflict started as a largely unarmed uprising against President Bashar al-Assad in March 2011. It has since turned into a full-blown civil war between government forces and opposition fighters, with an estimated death toll of some 280,000 people, according to the Observatory.