US-backed Iraqi forces said they began a push on Wednesday toward the mosque in Mosul's Old City, where Daesh declared its so-called "caliphate" three years ago.
The Counter Terrorism Service are up to 300 metres away from the medieval Grand al-Nuri Mosque, according to an Iraqi military statement.
The military had earlier said the forces had encircled the Daesh stronghold after taking over an area to the north of the territory earlier.
The forces had to dodge snipers and booby traps to get to the area, where more than 100,000 civilians are trapped.
The US-led coalition is providing air and ground support to the Mosul offensive that started on October 17, 2016.
Iraqi officials have expressed hope that the mosque could be captured by Eid al-Fitr, the festival marking the end of Ramadan, the Muslim fasting month. The first day of the Eid falls this year on June 25 or 26 in Iraq.
Daesh encircled in Old City
The army's 9th armoured division had seized the al-Shifaa district alongside the western bank of the Tigris river, a military statement said on Tuesday.
The fall of Shifaa means the Old City in the eastern half of Mosul is now surrounded by US-backed government forces, deployed north, west, south and across the river.
The battle for the Old City is becoming the deadliest in the eight-month-old offensive to capture Mosul, Daesh's de facto capital in Iraq.
The militants are moving stealthily in the Old City's maze of alleyways and narrow streets, through holes dug between houses, fighting back the advancing troops with sniper and mortar fire, booby traps and suicide bombers.
They have also covered many streets with sheets of cloth to obstruct air surveillance, making it difficult for the advancing troops to hit them without risking civilian lives.
"We are attacking simultaneously from different fronts to fraction them into smaller groups easier to fight," said an officer from the Federal Police, another force taking part in the assault on the Old City,
The Iraqi army estimates the number of Daesh fighters at no more than 300, down from nearly 6,000 in the city when the battle of Mosul started on October 17.
The fall of Mosul would, in effect, mark the end of the Iraqi half of the "caliphate" even though Daesh would continue to control territory west and south of the city, the largest they had gained hold of, in both Iraq and Syria.
The Iraqi government initially hoped to take Mosul by the end of 2016, but the campaign took longer as militants reinforced positions in civilian areas to fight back.
About 850,000 people, more than a third of the pre-war population of Mosul, have fled, seeking refuge with relatives or in camps, according to aid groups.