The Iraqi prime minister's statement coincides with a fresh offensive to dislodge Daesh from villages around Mosul, their last major stronghold in Iraq.
Iraq's Prime Minister Haider al-Abadi said on Thursday that Iraqi forces are advancing faster than expected in the offensive to recapture Mosul from Daesh.
The Iraqi government on Monday launched the offensive on Mosul, the country's second-largest city, two years after it fell to Daesh, who then declared a caliphate in parts of Iraq and Syria.
"The forces are pushing towards the town more quickly than we thought and more quickly than we had programmed in our campaign plan," Abadi said, speaking on a videoconference link to an international meeting in Paris co-hosted by France and Iraq on the future of Mosul following the start of the offensive this week.
Abadi's statement coincides with a fresh offensive by an Iraqi army elite unit and peshmerga fighters to dislodge Daesh from villages around Mosul, their last major stronghold in Iraq.
The operation is backed by air and ground support of the US-led coalition.
Howitzer and mortar fire started at 6:00 am (0300 GMT), hitting a group of Daesh-held villages around 20 kilometres (13 miles) north and east of Mosul, while helicopters flew overhead.
French President Francois Hollande said at Thursday's meeting that the terrorists 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. "We cannot allow those who were in Mosul to evaporate," he added.
Representatives from around 20 countries including the United States, Turkey, Gulf states and EU member states attended the Paris meeting co-chaired by French Foreign Minister Jean-Marc Ayrault and his Iraqi counterpart Ibrahim al-Jaafari.
The aim of the meeting was to discuss how to restore peace and stability to Mosul after Daesh has been routed.
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 Secretary of Defense Ashton Carter will be among 13 ministers at the talks, an aide to Le Drian said.
Some 30,000 troops are taking part in Iraq's largest military operation since the pullout of US troops in 2011.
Four days into the assault, the US-backed government and peshmerga forces are steadily recovering outlying territory before the big push into the city itself.
On the northern front, peshmerga shot down an unmanned drone aircraft with machine guns that came from the Daesh lines in the village of Nawaran a few kilometers away.
It was not clear if the drone, one to two metres (1.1 yard to 2.2 yards) wide, was carrying explosives or just on reconnaissance.