Many of those fleeing were injured as they tried to find a way out of Daesh-held districts amid fierce fighting in the city.
Thousands of civilians, many of them wounded, fled Daesh's last stronghold in western Mosul on Tuesday.
They reached the Iraqi forces' lines after an exhausting march through the desert, as government forces and their allies continue their military campaign in several neighbourhoods to purge Iraq's second biggest city of Daesh militants.
More than 10,000 civilians have fled Daesh-held districts since the coalition forces breached the city's southern limits on Thursday, Iraqi commanders said.
According to an army general, around 800 civilians arrived at the sector held by the Iraqi army on Tuesday morning.
TRT World's Nicole Johnston spoke with some of those who fled the city.
Iraqi forces close in on government buildings
US-backed Iraqi forces on Tuesday battled their way to within firing range of Mosul's main government buildings.
"The provincial council and the governorate building are within the firing range of the Rapid Response forces," a media officer with elite Interior Ministry units said.
Iraqi forces captured the eastern side of Mosul in January after 100 days of fighting. They launched their attack on the districts that lie west of the Tigris river on February 19.
Mosul is the last major Daesh bastion in Iraq. It was in Mosul in 2014 that the group's leader Abu Bakr al-Baghdadi declared a caliphate over parts of Iraq and neighbouring Syria.
The US commander in Iraq says he believes the US and Iranian-backed government coalition will recapture both Mosul and Raqqa, Daesh's de facto capital in Syria, within six months.