#MosulOp: Iraqi forces advancing 'faster than expected'
"We are advancing faster than we had expected and planned," Abadi said, speaking on a video conference link to an international meeting co-hosted by France and Iraq on the future of Mosul following the start of the offensive this week.
French Defence Minister Jean-Yves Le Drian had warned on Tuesday that the battle to retake Iraq's second-biggest city could take "months".
French President Francois Hollande told Thursday's meeting that the militants were already fleeing to Raqqa, their stronghold in neighbouring Syria.
"We can't afford mistakes in the pursuit of the terrorists who are already leaving Mosul for Raqqa," Hollande said, adding: "We cannot allow those who were in Mosul to evaporate."
The French president added: "Everything must be done to protect civilians who are exposed in combat zones and used as human shields" by IS fighters.
The long-awaited offensive on Mosul was launched on Monday, with some 30,000 troops involved in Iraq's largest military operation since the pullout of US troops in 2011.
Abadi told the meeting: "Our war in Mosul is an Iraqi war for the Iraqis, for the defence of Iraqi territory."
Representatives from around 20 countries including the US, Turkey, Iran, Gulf states and EU member states are attending the Paris meeting co-chaired by French Foreign Minister Jean-Marc Ayrault and his Iraqi counterpart Ibrahim al-Jaafari.
Thursday's talks come ahead of a meeting in Paris next Tuesday of the coalition's defence ministers to assess progress in the Mosul offensive.
US Defence Secretary Ashton Carter will be among 13 ministers at the talks, an aide to Le Drian said.
Mosul, held by the militants since June 2014, was where IS leader Abu Bakr al-Baghdadi proclaimed a "caliphate" straddling Iraq and Syria that month.
"The battle for Mosul is decisive because it is hitting Daesh in the heart of its sanctuary where it wanted to build its caliphate," said Hollande, using an alternative name for IS.
The city's loss is widely predicted to deal a death blow to the group's ambitions as a land-holding force in Iraq.