Iraqi Army and police units advanced through populated western districts, fighting tough street battles, and announced they had captured Mosul's southernmost bridge, Reuters reported.
Once repaired, the bridge could help bring reinforcements and supplies from the eastern side, piling pressure on the Daesh terrorists dug in the western side among 750,000 civilians.
Iraqi forces captured eastern Mosul in January, after 100 days of fighting. They launched their attack on the districts that lie west of the Tigris a week ago.
If they defeat Daesh terrorist group in Mosul, that would crush the Iraq wing of the caliphate that the group's leader Abu Bakr al-Baghdadi declared in 2014 over parts of Iraq and neighboring Syria.
Since government forces broke through the city's southern limits on Thursday, more than 10,000 civilians have fled Daesh-held areas, seeking medical assistance, food and water, Iraqi commanders said.
About 1,000 civilians arrived in the early hours of Monday at the sector held by the Counter Terrorism Service (CTS), the wounded taken to the clinic of this elite unit, while men were screened to make sure they are not Daesh members.
Those who managed to escape have had to walk through the desert for at least an hour to reach government lines.
Several thousand terrorists, including many who traveled from Western countries to join up, are believed to be still in Mosul, prepared for a fierce standoff amid a remaining civilian population of 750,000.
The United Nations World Food Programme said on Monday it was extremely concerned about dire humanitarian situation facing families in western Mosul.