Commanders said that progress in the densely populated warren of alleyways was slow but that government forces had made new gains from IS in the heart of their last major urban bastion in Iraq.
"Our forces are 800 metres (yards) from the mosque," said Captain Firas al-Zuwaidi, spokesman for the interior ministry's elite Rapid Response Force.
He was referring to the Al-Nuri Mosque, where IS leader Abu Bakr al-Baghdadi declared the cross-border "caliphate" spanning jihadist-controlled territory in Iraq and Syria in his sole public appearance in July 2014.
"The fighting is street by street, house by house," he said, as the sound of mortar fire rang out from the heart of Iraq's second city.
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The battle for the Old City was always expected to be the toughest of the campaign to retake Mosul from IS, further complicated by the presence of hundreds of thousands of civilians believed to have stayed on under jihadist rule.
Iraqi forces launched the huge operation last October, retaking the east of the city in January before setting their sights on the smaller but more densely populated west.
The Rapid Response Force is being backed up by the federal police who have made steady gains in recent days.
They have now taken the Al-Arbiaa market and a grain silo overlooking the Old City, federal police commander Lieutenant General Raed Shakir Jawdat said today.
That came after Jawdat announced the capture of the Al-Basha Mosque and the Bab al-Saray market yesterday.
Iraqi forces had already taken a string of key targets in west Mosul, including the airport, the train station, Mosul Museum and the provincial government headquarters.