"The time of victory has come and operations to liberate Mosul have started," he said in an address broadcast by the Iraqiya channel.
"Today I declare the start of these victorious operations to free you from the violence and terrorism of Daesh (IS)," he said, addressing residents of the Mosul region.
Prime Minister al-Abadi vowed on Monday that only army and police forces would enter Mosul as he announced the start of operations to retake the jihadist-held city.
"The force leading liberation operations is the brave Iraqi army with the national police and they are the ones that will enter Mosul, not others," he said on state television.
The Iraqi army dropped tens of thousands of leaflets over Mosul before dawn on Sunday, warning residents that an offensive to recapture their city from Islamic State was in its final stages of preparation, according to a military statement in Baghdad.
The leaflets carried several messages, one of them assuring the population that advancing army units and air strikes "will not target civilians" and another telling them to avoid known locations of Islamic State militants.
Islamic State fighters are dug in, expected to fight hard and have a history of forcing civilians to stay in harm's way during previous battles to defend territory.
Reflecting the authorities' concerns over a mass exodus that would complicate the offensive, the leaflets told residents "to stay at home and not to believe rumours spread by Daesh" to cause panic, referring to Islamic State by its Arabic acronym.
With a pre-war population of around 2 million, Mosul is around 4-5 times the size of any other city recaptured so far from the militants, who swept through northern Iraq in 2014 and also hold a swathe of Syria.
The UN last week said it was bracing for the world's biggest and most complex humanitarian effort in the battle for the city, which could make up to 1 million people homeless and see civilians used as human shields or even gassed.
"Keep calm and tell your children that it is only a game or thunder before the rain," a leaflet said. "Women should not scream or shout, to preserve the children's spirit."
"If you see an army unit, stay at least 25 metres away and avoid any sudden movements," another said.
