A top special forces commander told AFP that while the Nuri mosque -- which was blown up by the ISIS group last week -- was close to being recaptured, it had not been retaken yet.
"Counter-Terrorism Service forces control the Nuri mosque and Al-Hadba (minaret)," the Joint Operations Command said in a statement.
But Staff Lieutenant General Abdulwahab al-Saadi said that while Iraqi forces were close to retaking the mosque, they were still some 20 metres (yards) away.
The mosque and its famed Al-Hadba (hunchback) leaning minaret were Mosul landmarks and also held major significance in the history of ISIS rule in Iraq.
Baghdadi appeared during Friday prayers at Nuri mosque in 2014, soon after ISIS seized Iraq's second city, calling on Muslims to obey him.
Three years later, Baghdadi's fate and whereabouts remain unknown, and ISIS has lost much of the territory it overran in 2014.
The terrorists blew up the mosque and minaret on June 21 as they put up increasingly desperate resistance to the advance of Iraqi forces.
Officials from Iraq and the US-led anti-ISIS coalition said the destruction of the site was a sign of the terrorist group's imminent loss of Mosul, with Prime Minister Haider al-Abadi calling it an "official declaration of defeat".
The loss of the iconic 12th century minaret -- one of the country's most recognisable monuments sometimes referred to as Iraq's Tower of Pisa -- left the country in shock.
But the destruction had been widely anticipated, with commanders saying ISIS, also known as ISIS and Daesh, would not have allowed Iraqi forces to score a hugely symbolic victory by recapturing the site.
ISIS claimed on its Amaq propaganda agency that the site was hit in a US air strike, but the US-led coalition said it was the terrorists who had "destroyed one of Mosul and Iraq's great treasures".
- Heritage destroyed -
The mosque in Mosul's Old City was the latest in a long list of priceless heritage and historical monuments destroyed by ISIS during its three-year rule over swathes of Iraq and Syria.
The minaret, which was completed in 1172 and had been listing for centuries, is featured on Iraq's 10,000-dinar banknote and was the main symbol of Iraq's second city -- giving its name to countless restaurants, companies and even sports clubs in Mosul.
After seizing Iraq's Sunni Arab heartland in June 2014, ISIS reportedly rigged the Hadba with explosives but was prevented from blowing it up by the local population. The terrorists consider the reverence of objects, including of such sites, as heresy.
The mosque's destruction came three days after government forces launched an assault on the Old City, the last district of Mosul still under ISIS control.
About 100,000 residents are believed to still be trapped in the district by ISIS, which has been using civilians as human shields to defend its last redoubt in Mosul.
The area still controlled by the terrorists is small but its narrow streets and the presence of so many civilians has made the operation perilous.
The terrorists have been offering fierce resistance in the Old City, with barrages of mortar fire and a huge number of booby traps slowing the Iraqi advance.
While Iraqi forces have made good progress to reach the Nuri mosque, Iraqi commanders have warned that the battle for the Old City is far from over.