An on-screen headline on Iraqiya news on Sunday said Iraqi special forces have "raised the Iraqi flag on the Tigris riverbank in the Old City of Mosul".
About 100 ISIL fighters had earlier been reported to be trapped in a sliver of the Old City along the Tigris.
Many of them threw themselves into the river as they faced imminent defeat on Sunday, according to Reuters news agency.
The agency also reported plumes of smoke over the Old City and decaying corpses of ISIL fighters lying on its streets. Scattered bursts of gunfire could be heard and several air strikes were carried out, it said.
Iraqi commanders said on Saturday that ISIL controlled just two blocks, and that their troops were just "tens of metres" away from defeating ISIL.
Officials have made similar pronouncements of victory being imminent over the past week, but progress appears to have slowed in recent days with ISIL fighters placing booby traps and bombs to block advancing troops.
'Not over yet'
Al Jazeera's Charles Stratford, reporting from Erbil in northern Iraq, said that fighting is still ongoing away from the Tigris River.
"It's not over yet," he said. "This area that Iraqi forces have reached on the Tigris River does not include these two blocks where heavy fighting continues."
As the battle rages on, the humanitarian crisis in Mosul is worsening, he said.
"We are seeing more civilians coming across the front line," he said. "Horrific stories are being told. Many of them are malnourished and seriously dehydrated. Very many of them are deeply traumatised by the months they've spent hiding in their homes."
The fall of Mosul would be the biggest defeat yet for ISIL three years after it seized the city in a lightning offensive.
With air support from the US-led coalition, Iraqi forces launched the battle for Mosul in October, retaking the eastern part of the city in January and starting the operation for its western part the next month.
The eight-month battle for Mosul has ruined parts of the city, killed thousands of civilians and displaced nearly one million people.
On Saturday, jubilant police forces were seen flashing V-for-victory signs in Mosul and posing for selfies in front of each other, holding up ISIL's black flag upside down.
Distraught women and children were seen clutching what few belongings they could carry. Hungry and haggard, they told AFP they had spent months being held as human shields by ISIL fighters.
As the Iraqi forces make their final push, approximately half of the population of the city is still displaced, the Norwegian Refugee Council (NRC) said.
Tens of thousands of people are likely to return to the city in the near future, placing pressure on the Iraqi government and the international community to begin rebuilding immediately.
"People from every ethnic, religious and socioeconomic group in Iraq have suffered as a result of this conflict," said Heidi Diedrich, the NRC's country director.
"It is the responsibility of the international community now to help them rebuild their country and repair the divisions that helped to create the conflict in the first place."
The UN predicts it will cost more than $1bn to repair basic infrastructure in Mosul.
In some of the worst-affected areas, almost no buildings appear to have escaped damage and Mosul's dense construction means the extent of the devastation might be underestimated, UN officials said.
Mosul is the ISIL's last urban bastion in Iraq.
While the armed group has lost much of the territory it once held in Iraq, Al Jazeera's Stratford said ISIL still controls a number of towns in Iraq, including Tal Afar, west of Mosul, and Al Qa'im on the Syria-Iraq border.
"By no means does this seemingly imminent victory by Iraqi forces in Mosul mean the end of ISIL in Iraq," he said. "There's still a lot more to do."
Source: Al Jazeera and news agencies