Haider al-Abadi said the move showed "rapprochement" and unity of purpose between Iraqi and Kurdish forces.
His comments came as Kurdish fighters launched a large-scale operation east and north of Mosul.
The Iraqi army has been moving from the south, and special forces have now joined the offensive.
Mosul has been in the hands of IS since 2014 and is the militants' last major Iraqi stronghold.
The offensive to retake it began on Monday. Up to 1.5 million civilians are thought to still be inside the city. Those inside report that they are running out of basic supplies.
There are reports that some IS leaders have fled, but there are thought to be up to 5,000 IS fighters still in the city.
The Iraqi prime minister made his comments via video-link to an international meeting in Paris on the future of Mosul.
"The forces are pushing towards the town more quickly than we thought and more quickly than we had programmed in our campaign plan," he said.
He hailed co-operation between the army and Kurdish troops, saying they were "fighting harmoniously together" to free Iraqi territory from IS.
French President Francois Hollande, hosting the meeting, warned that IS fighters were fleeing to Raqqa, the militant group's stronghold in Syria, and said efforts must be made to stop them.
The whereabouts of IS leader Abu Bakr al-Baghdadi are unknown. Some reports say he is in Mosul, but others say he has fled the northern Iraqi city.
Under cover of darkness we joined a long convoy of vehicles setting out from a Kurdish base on Bashiq Mountain, about 15km (nine miles) from Mosul.
We snaked towards areas under IS control, along a route that had been checked for roadside bombs. There were hundreds of pick-up trucks with troops and some with vehicle-mounted machine guns. Along the way we saw some American special forces.
The aim is to clear the town of Bashiqa and 20 surrounding villages, most of which are deserted apart from IS fighters. The offensive includes some veteran Kurdish fighters who once fought against Saddam Hussein.
Before leaving the base, senior commander Shex Jaffar Shex Mustafa told us they were ill equipped for the battle and did not even have enough body armour. "All of our victories are made by our blood," he said.
The general in charge urged his men to go slowly, to avoid casualties. "We hope to survive this battle," one fighter told me, "but we are facing an enemy that hopes to die."
On Thursday, Kurdish fighters began moving on three fronts east and north of Mosul.
"The objectives are to clear a number of nearby villages and secure control of strategic areas to further restrict Isil's [IS] movements," a statement said.
Iraqi special forces, supported by air strikes carried out by a US-led coalition, also began a pre-dawn advance on the town of Bartella, which is less than 15km (10 miles) from Mosul.
"We started breaching Bartella early today. There is only 750m to cover to reach the centre," Lieutenant General Abdelwahab al-Saadi, who is commanding operations in the area, told AFP news agency by telephone.
IS militants responded to the advance with several suicide car bombs, AP reported, but there was no information about casualties.
Officials have warned that the push to take Mosul could take weeks or months, with IS fighters appearing to be putting up stiff resistance in some areas.
There are also warnings that the group could use human shields or chemical weapons.
Addressing the Paris meeting, Mr Abadi promised support for civilians affected by the fighting.
The UN on Tuesday warned that up to 200,000 people could be displaced in the first two weeks of the military operation in Mosul.
Camps are being built in the south, east and north of Mosul in preparation for a flood of people fleeing the city.
The head of delegation in Iraq for the International Committee of the Red Cross, Katharina Ritz, said she was concerned fleeing civilians could be caught up in the fighting.
"We call on all the parties to respect, to protect them, to help them to access safe areas," she said.

Sum: The operation to retake the Iraqi city of Mosul from so-called Islamic State militants is progressing faster than planned, the Iraqi prime minister says.


Usk in south Wales recorded a top temperature of 19.9C (68F) on Monday, while many in England, Northern Ireland and other parts of Wales also got plenty of sunshine.
However, the highest temperatures of the Easter weekend were recorded in Scotland, with those in Aboyne, Aberdeenshire, hitting 20.7C (69F) on Sunday - the hottest day of the year so far.

Sum:
Large parts of the UK have enjoyed a warm end to the Easter weekend - with temperatures peaking at almost 21C (70F) in some areas of southern England.