Troops from the army's 9th Division and the police's Rapid Response Force were now advancing on the Musharifa, Kanisa and Haramat districts from the north, the BBC reported.
They will join troops who were pushing into the Old City from the south.
On Sunday, Army Chief of Staff Lt Gen Othman al-Ghanmi told an Iraqi daily that he expected the battle in the west to be completed "in a maximum of three weeks" despite fierce resistance from militants in the Old City.
The troops launched a major offensive to recapture Mosul, the last major IS stronghold in Iraq, in October.
Supported by the US-led coalition air strikes and military advisers, they managed to take full control of the eastern half of Mosul in January and started an assault on the west in February.
More than 580,000 civilians have been displaced since the operation to recapture it began, among them 419,000 from western Mosul, according to Iraqi authorities.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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Doraiah Chowdary Vundavally is a Software engineer at VTech . He is the news editor of SocialNews.XYZ and Freelance writer-contributes Telugu and English Columns on Films, Politics, and Gossips. He is the primary contributor for South Cinema Section of SocialNews.XYZ. His mission is to help to develop SocialNews.XYZ into a News website that has no bias or judgement towards any.