Haider al-Abadi says army took back eastern part of city, day after defence ministry retracted earlier claim of victory.
Iraq’s prime minister, Haider al-Abadi, said eastern Mosul has been "fully liberated" from the Islamic State of Iraq and the Levant group.
Abadi’s announcement on Tuesday came 100 days after a US-backed operation to retake the city began.
In a news conference, Abadi hailed the "unmatched heroism of all security forces factions" and public support for the operation.
"Daesh has quickly collapsed and no one expected such collapse," Abadi said, using the Arabic acronym of ISIL, also known as ISIS. "The heroism of our security forces was behind Daesh’s defeat."
A day earlier, the Iraqi defence ministry issued a statement retracting an earlier claim in which it announced the "liberation of the eastern part of Mosul" from ISIL, calling it a "mistake".
On its website on Monday, the army said that the armed forces succeeded in liberating the left bank of the city completely, "after inflicting heavy losses in lives and equipment to the enemy".
However, in a later statement on Monday, the defence ministry said that the 9th and 16th army brigades were still locked in fierce battles against ISIL in the Al-Rashidiya district, while Iraqi troops were still clearing other neighbourhoods and clashing with ISIL fighters.
Asked how long it will take to liberate the western side of the city, Abadi told the Associated Press news agency: "I can’t tell now, but we are capable of doing so and we will do so."
International and Iraqi aid groups have expressed concern for the estimated 750,000 people still in the city’s ISIL-held west.
The UN Humanitarian Coordinator for Iraq, Lise Grande, voiced fears for civilians in the western half of the city in a statement signed by 20 international and local aid groups.
The cost of food and basic goods has been soaring, supplies of water and electricity were intermittent, and some residents were being forced to burn furniture to keep warm, Grande said.
"We hope that everything is done to protect the hundreds of thousands of people who are across the river in the west," Grande said in the statement.
"We know that they are at extreme risk and we fear for their lives."
The statement called on warring parties "to uphold their obligations under international humanitarian law to protect civilians and ensure they have access to life-saving assistance".
In Geneva, Ravina Shamdasani, a spokeswoman for the UN human rights office said it had received "reasonable corroboration" for a report that 19 civilians were killed in an air strike in the al-Jadida neighbourhood of ISIL-controlled western Mosul last week.
"Attributing responsibility for air strikes is very difficult," Shamdasani said, adding that "it is clear that civilians are being killed in air strikes".
The UN human rights office also said ISIL fighters have taken over "many hospitals" in western Mosul and are using them as military bases. It said the group is diverting food, water and medicine to its fighters.
Mosul, Iraq’s second-largest city and the ISIL’s last urban stronghold in the country, fell into the hands of the the armed group in the summer of 2014, when the fighters captured large swaths of northern and western Iraq.
Hundreds of civilians fled from the northeastern Rashidiya neighbourhood on foot as Iraqi helicopters circled overhead and fired on fighters.
Meanwhile, Abadi renewed his promise to investigate allegations of human rights violations by security forces in conflict areas and bring those responsible to trial, a day after ordering a probe into a video on social media purportedly showing government troops beating and killing at least three ISIL suspects in Mosul.
On Monday, a provincial investigative committee in the country’s western Anbar province concluded its probe into human rights violations in June near the town of Fallujah. It found that a member of a Shia militia killed 17 civilians, he said.
The fighter, affiliated with the Badr group, is now in detention and awaiting trial, Abadi said.