MOSUL (AFP) - Iraqi forces engaged in "heavy" fighting with the Islamic State in Iraq and Syria (ISIS) group on Monday (July 10) as they battled to clear the last extremist-held pockets in Mosul's Old City, a senior commander said.

Iraqi Prime Minister Haider al-Abadi visited Mosul on Sunday to hail his forces for securing victory in the city but said he was holding off on making a formal announcement of victory until the last ISIS resistance was eliminated.

Lieutenant General Sami al-Aridhi, a senior commander in the elite Counter-Terrorism Service, said the ISIS-held territory had been reduced to an area of the Old City of about 200 by 100 metres.

"They do not accept to surrender," Aridhi told AFP. "They say in a loud voice: 'We will not surrender, we want to die.'"

But "operations are in their final stages," and "it is likely that (the fighting) will end today," Aridhi said.

That final push poses significant danger to civilians in the area, whom the jihadists may use as human shields.

Aridhi said his forces had information that there were between 3,000 and 4,000 civilians in the small area still under ISIS control but that could not be independently confirmed.

ISIS overran large areas of the country in 2014, but Iraqi forces backed by US-led air strikes have since regained much of the territory they lost.

The recapture of Mosul will not however mark the end of the threat posed by ISIS, which controls territory elsewhere in Iraq and is able to carry out frequent bombings in government-held areas.