The push comes after the US-backed Iraqi forces advance into western districts of the city was paused for 48 hours due to bad weather.
US-backed Iraqi forces on Sunday launched a new push toward the Daesh-held old city centre of western Mosul, an Iraqi military spokesman said.
The Iraqi army is fighting its way toward the old centre of the city, advancing from the south and the southwest, Brigadier-General Yahya Rasool, spokesman for the joint operations command, told state-run television.
The Iraqi forces backed by US-led coalition had recaptured the eastern side of the Daesh bastion in January after 100 days of fighting. They launched the attack on the districts that lie west of the Tigris river on February 19.
Their advance in western Mosul paused over the past 48 hours because of bad weather.
TRT World's Nicole Johnston reports from western Mosul.
Battle to get tougher
Iraqi security forces are progressing as planned in the fight to retake Mosul from Daesh but the battle will get tougher as they get closer to the city center, a US general said on Saturday.
"We are on (a good) timeline and we are fairly confident that the Iraqis are learning every day, and we are fairly confident they are going to continue to progress well," Brigadier General Rick Uribe, a deputy commanding general for coalition land forces.
But "make no mistake about it, as we get closer to the center of the city, it just gets tougher and tougher because of the terrain that the Iraqi security forces are about to enter," Uribe said.
The oldest parts of Mosul are packed with buildings and crisscrossed with narrow streets that will make fighting more intense.
Defeating Daesh in Mosul would crush the Iraqi wing of the caliphate declared by the group's leader, Abu Bakr al-Baghdadi, in 2014, over parts of Iraq and Syria.