Updated at 4.30pm

Islamic State's "state of falsehood" has come to an end, Iraqi Prime Minister Haider al-Abadi said today after Iraqi troops captured the wrecked historic mosque of Mosul in which the insurgents declared their self-styled caliphate three years ago.

"The return of al-Nuri Mosque and al-Hadba minaret to the fold of the nation marks the end of the Daesh state of falsehood," Abadi said in a statement, referring to the ultra-hardline Sunni group by an Arabic acronym.

He said Iraqi forces would continue to hunt Islamic State's fighters "to kill them and detain them, down to the last one".

The insurgents blew up the medieval mosque and its famed leaning minaret a week ago as US-backed Iraqi forces advanced towards it. Their black flag had been flying from al-Hadba (The Hunchback) minaret since June 2014.

Special forces entered the compound and took control of the surrounding streets this afternoon, following a dawn push into the area.

Earlier, special forces Major General Sami al-Aridi warned the site will need to be cleared by engineering teams as IS fighters likely rigged it with explosives.

Iraqi forces are pushing through the last IS-held neighbourhood in Mosul, the so-called Old City, to the west of the Tigris River.

The mosque is hugely symbolic - from its pulpit, IS leader Abu Bakr al-Baghdadi in July 2014 declared a self-styled "caliphate" on IS-held territories in Syria and Iraq.

Damaged and destroyed houses dot the route Iraqi forces have carved into the congested district - along a landscape of destruction where the stench of rotting bodies rises from under the rubble.

Iraqi and coalition officials said IS blew up the mosque complex last week.

IS has blamed a US air strike for the destruction.

After months of fighting, the IS hold in Mosul has shrunk to less than two square kilometres of territory but the advances have come at considerable cost.

"There are hundreds of bodies under the rubble," said special forces Major Dhia Thamir, deployed inside the Old City.

He added that all the dead bodies along the special forces' route were of IS fighters.

Mr al-Aridi acknowledged that some civilians have been killed by air strikes and artillery in the fight for the Old City.

"Of course there is collateral damage, it is always this way in war," he said.

"The houses are very old," he said, referring to the Old City, "so any bombardment causes them to collapse completely."

In Baghdad, state TV declared the capture of the al-Nuri Mosque with an urgent text scroll that said: "The State of Myth Has Fallen."