CTS says it could take at least four to five days of fighting to capture the last handful of neighbourhoods along the banks of the Tigris River.
A fierce battle between Daesh and Iraqi forces rages on in the district around Mosul's Grand al Nuri Mosque as dozens of civilians, mostly women, children and the elderly flee the Old City.
Iraqi Prime Minister Hailer al-Abadi declared the end of Daesh's caliphate, which he called "a state of falsehoood", on Thursday after Commanders of Iraq's Counter Terrorism Service (CTS) captured the ground of the ruined 850-year-old Grand al Nuri Mosque.
The leaning minaret of the mosque survived conquests by the Mongols and the Ottomans, neglect under Saddam Hussein, and air raids during the Iran-Iraq War and the US invasion in 2003.
However, after three years of Daesh rule, it is now little more than a pile of stones at the centre of a shattered city.
TRT World's Nicole Johnston reports from the frontline of the battle in Mosul.
The CTS on Friday cautioned that non-Iraqi Daesh militants dug in among thousands of civilians and likely to fight to the death.
CTS Major General Maan al-Saadi said that it could take at least four to five days of fighting to capture the last handful of neighbourhoods along the banks of the Tigris River, defended by about 200 militants.
"The advance continues to Midan neighbourhood," he said, adding that "controlling it means we have reached the Tigris River."
The fight for the city may be almost over, but many civilians are still trapped in Daesh's last pockets of resistance.
The insurgent positions in Mosul is several hundred metres wide and thousands of civilians are trapped in harrowing conditions, with little food, water, medicine and no access to health services, according to those who managed to flee.
Those who escaped on Friday streamed through alleyways near the mosque, which Daesh fighters blew up a week ago.
They scrambled over mounds of rubble in the street, carrying small children and helping the elderly across.
"I hear victory speeches on the radio but I cannot help feeling sad when you see people without homes and others fleeing with their children under the blazing sun," said Mahmoud, a taxi driver in the eastern side of Mosul which was liberated from the militants during the first 100 days of the campaign.
The United Nations called on the Iraqi government on Friday to intervene and halt "imminent" forced evictions of many people suspected of having ties to Daesh in Mosul.
Hundreds of families have received threatening letters laying down a deadline for leaving, mainly under tribal agreements, which amount to "acts of vengeance", UN human rights spokesperson Rupert Colville said.
"We urge the Iraqi Government to take action to halt such imminent evictions or any type of collective punishment, and to reinforce the formal justice system to bring perpetrators to justice," he told a Geneva news briefing.