Iraqi forces have retaken the main government compound in the centre of Fallujah from the Islamic State of Iraq and the Levant (ISIL) group, top commanders say.

The government lost control of Fallujah in 2014, months before ISIL took Iraq's second largest city, Mosul, and swept across large parts of the country.

"The counterterrorism service and the rapid response forces have retaken the government compound in the centre of Fallujah," the operation's overall commander, Lieutenant-General Abdulwahab al-Saadi, told AFP on Friday.

The Iraqi flag is now raised on top of the building, symbolising government control.

Raed Shaker Jawdat, Iraq's federal police chief, confirmed the advance, which marks a significant step in the nearly four-week-old offensive to retake the city in Anbar province.

"The liberation of the government compound, which is the main landmark in the city, symbolises the restoration of the state's authority" in Fallujah, he said.

Both commanders said their forces had met limited resistance from ISIL fighters during the push into the city centre.

"This is a very significant development," said Al Jazeera's Omar Al Saleh, who has reported extensively on the conflict in Iraq.

"It is a big moral boost for Iraqi soldiers."

Government troops and Shia units known as the Popular Mobilisation Forces are leading the campaign to retake the city from ISIL.

They are supported by US-led coalition air strikes.

"In different parts of Fallujah ISIL still remains," said Saleh, "Iraqi forces still have a tough few days ahead."

It is believed that up to 90,000 civilians are still inside Fallujah. And the clashes between the government forces and ISIL are causing casualties.

Al Jazeera's Saleh said the death toll so far is based on estimates by medical sources from the city of Fallujah.

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"They say it is in the hundreds," he said.

Although the Iraqi government previously said it had a particular strategy to establish safe corridors for civilians in the city centre to leave, many have been reluctant to go for fear of how they may be treated by the Shia units.

The humanitarian crisis in Iraq has been dubbed one of the world's worst by the UN.

Since the beginning of the present conflict in 2014, more than 3.4 million people have been internally displaced and 2.6 million have fled Iraq.