The assault is aimed at sealing the siege of the Old City, where die-hard jihadists holding huge numbers of civilians hostage are preparing for a bloody last stand.
Forces from the army, the interior ministry and the police "began breaching the western side from the north," the Joint Operations Command (JOC) coordinating the war against IS said in a statement.
"Now your sons are fighting and striking the enemy's defences... They rejoice in victory or martyrdom for the sake of liberating the rest of the city of Mosul from Daesh (IS) terrorists," it said.
The federal police issued a statement confirming the new operation, which comes after a relative lull in fighting around the Old City where most remaining jihadists are believed to be holed up.
It said Iraqi forces had already captured a small outlying village called Hsunah and a nearby gas factory.
Today's operation opens a new front in the effort to wrest back west Mosul from IS which started in mid-February and saw thousands of Iraqi forces retake most southern and western neighbourhoods.
The United Nations said up to 400,000 people might be trapped in the densely populated Old City, which lies just west of the Tigris River that divides Mosul.
The Iraqi immigration ministry said this week that the number of people who were displaced since the start of the offensive on Mosul on October 17 had topped 600,000.
The vast majority of them fled homes on the west side of the Tigris, where the fighting has been more intense than in east Mosul, which was declared retaken by the government in January.
The recapture of Mosul by the Iraqi security forces would deal a death blow to the "caliphate" IS proclaimed over large parts of Syria and Iraq nearly three years ago.
It would represent a major symbolic setback for the group whose unprecedented experiment in jihadist statehood was heralded by the conquest of Mosul in June 2014.
The northern city is where Iraq-born IS supremo Abu Bakr al-Baghdadi - who has urged his men to defend Mosul to the death - made his only public appearance in July that year.
The jihadists have in recent days carried out diversionary attacks against security forces from their desert hideouts in the western province of Anbar.
At least 26 members of the army, police, tribal forces and border guard died in the attacks but the jihadists' "state" has looked doomed for months.
Observers have warned that, with other anti-IS forces also pressing a major offensive on their last major Syrian bastion of Raqa, the jihadists could increasingly revert to guerrilla tactics and bombings of civilian targets.
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