Update 7.39: The US-led coalition has congratulated Iraqi forces on retaking Mosul from the Islamic State group after Iraq’s prime minister declared victory in the city.
US Central Command said "while there are still areas of the Old City of Mosul that must be back-cleared of explosive devices and possible ISIS fighters in hiding," Iraqi forces "have Mosul now firmly under their control."
The coalition has provided crucial air support to Iraqi forces since they launched the Mosul offensive in October.
Lieutenant General Stephen Townsend said "make no mistake; this victory alone does not eliminate ISIS and there is still a tough fight ahead," using another acronym for Islamic State. But he said the loss of the city "is a decisive blow".
Speaking from a small base on the edge of the Old City, where heavy clashes have been under way for days, Haider al-Abadi said Iraqi forces had achieved victory "by the blood of our martyrs".
He has made similar announcements in recent days despite ongoing clashes, and visited Mosul on Sunday to congratulate Iraqi troops.
Heavy fighting was still under way just a few hours before he spoke on Monday.
US-backed Iraqi forces launched a massive operation to retake Mosul in October.
The battle for Mosul killed thousands and displaced more than 897,000 people.
In this video, the Washington Post investigates why it took so long for Iraqi forces to regain control of its second largest city from Islamic State militants and what challenges remain now that Mosul has fallen.
Earlier: The US-led coalition has said Iraqi forces have retaken all of Mosul from the Islamic State group.
Iraq’s prime minister has returned to Mosul and declared "total victory" in the fight against the Islamic State group there, though some fighting is expected to continue.
Prime Minister Haider al-Abadi has congratulated Iraqi troops on their "victory" on previous occasions despite ongoing clashes.
The latest announcement came in a statement posted on Twitter.
Hours earlier, Associated Press reporters had seen heavy fighting still under way.
It was not immediately clear if the clashes had ended.
US-backed Iraqi forces launched a massive operation to retake Mosul in October, and in recent days they had confined the remaining few hundred militants in an area measuring less than a square kilometre.
Mr al-Abadi visited Mosul on Sunday to congratulate the troops, even as fighting still raged nearby.