"We are advancing faster than we had expected and planned," Abadi said, speaking on a videoconference link to an international meeting co-hosted by France and Iraq on the future of Mosul following the start of the offensive this week, AFP reported.
"Our war in Mosul is an Iraqi war for the Iraqis, for the defense of Iraqi territory,” Abadi told the meeting.
Representatives from around 20 countries including the US, Turkey, Iran, the Persian Gulf states and EU members 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 defense ministers to assess progress in the Mosul offensive.
Four days into the assault on Mosul, Iraqi and Kurdish forces are steadily recovering outlying territory before the big push into the city itself, expected to be the biggest battle in Iraq since the 2003 US-led invasion of the Arab country.