The announcement of the recapture of the mosque -- which the Islamic State group blew up last week as Iraqi forces closed in -- comes three years to the day after the jihadists declared a "caliphate" straddling Iraq and Syria.
"Counter-Terrorism Service forces control the Nuri mosque and Al-Hadba (minaret)," the Joint Operations Command said in a statement.
After a senior special forces commander said the mosque had not in fact been retaken, the operations command clarified that it meant Iraqi forces had isolated the area and were "advancing toward the completion of the goals."
Iraqiya state TV carried a banner on Thursday announcing the "fall of the mythical state" -- a play in Arabic on the IS title "state of the caliphate."
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Baghdadi appeared at Friday prayers at the Nuri mosque in 2014, soon after IS seized Iraq's second city, calling on Muslims to obey him.
Three years later, Baghdadi's fate and whereabouts remain unknown, and IS has lost much of the territory it overran in 2014.
The jihadists blew up the mosque and minaret on June 21 as they put up increasingly desperate resistance to the advance of Iraqi forces.
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 IS would not have allowed Iraqi forces to score a hugely symbolic victory by recapturing the site.
IS 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 jihadists who had "destroyed one of Mosul and Iraq's great treasures".
The mosque in Mosul's Old City was the latest in a long list of priceless heritage and historical monuments destroyed by IS 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.
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