Speaking on a visit to the front line to the east of the city, Haider al-Abadi said government-led forces “will not retreat and will not be broken,” BBC qouted him as saying.
He said his message to the people of Mosul was “we will liberate you soon”.
The city has been under the IS control for more than two years.
“My message to IS, if they want to save their lives, they should lay down their weapons now,” the Prime Minister told media.
Government forces on Saturday also gained control of Hammam al-Alil, about 15 km south of Mosul on the Tigris river, despite fierce resistance, the army said.
Lt. Gen. Raed Shakir Jawdat said security forces were in control of the centre of the town, but did not say whether the IS militants had been pushed out completely.
The operation to take back control of Mosul continued as government forces tried to clear the eastern districts, including al-Zahra, which they entered on Friday.
Satellite images of Mosul reveal how IS fighters constructed multiple barricades across key routes into the northern Iraqi city.
Concrete barricades and rubble can be seen blocking key streets, while buildings near de-facto capital airport were levelled for line-of-sight reasons.
Mosul fell to the jihadis in June 2014 and their leader, Abu Bakr al-Baghdadi, chose a mosque in the city as a place to proclaim the establishment of a “caliphate”.
Before the offensive began on 17 October, there were believed to be between 3,000 and 5,000 militants remaining in Mosul, along with up to 1.5 million civilians.—IANS