But as they lose most of the territory they brought under their control about three years ago, ISIS militants are making use of hit-and-run and surprise attacks.
The Iraqi forces launched their campaign to recapture Mosul in October, and since then ISIL has gone from holding the entire city to being trapped between security forces and the Tigris River on its western side. Some units remain up to 150 yards from the river. Iraqi forces are backed by air strikes and advisers of the US-led coalition fighting IS in Iraq and Syria since 2014.
The almost nine-month battle for Mosul has ruined parts of the city, killed thousands of civilians and displaced almost one million people.
Isis militants were driven out of the city in northern Iraq this weekend after months of intense battle with Iraqi army.
French President Emmanuel Macron was among the first to hail the victory of Iraqi forces in Mosul on Sunday, praising the fighters - including French troops in the coalition - who had made it possible.
Dozens of IS insurgents were killed on Saturday and others tried to escape by swimming across Tigris, state TV said.
However the ISIS Amaq news agency claimed "fierce fighting" was ongoing around the Maydan district.
There were a large number of roadside bombs and booby-trapped buildings, in addition to IS snipers taking position in the buildings and narrow alleys of heavily-populated neighbourhoods, where thousands of civilians still live under the IS rule.
"It is a major blow to IS's prestige", said David Witty, an analyst and retired USA special forces colonel.
Al-Iraqia TV quoted al-Abadi as saying he "congratulates the fighters and the people on the big victory" in the key city, even as fighting continued in pockets. The militants destroyed the mosque and its famed minaret as Iraqi forces closed in last month.
The Iraqi government did not reveal casualty figures, but a funding request from the US Department of Defense said the elite Counter Terrorism Service, which has spearheaded the fight in Mosul, had suffered 40% losses. An estimated 1 million people had fled the city during the lengthy battle and thousands were killed.
"For children and their families to process these horrors and rebuild their lives, psychological support will be absolutely crucial", said Ana Locsin, Save the Children's Iraq country director.