A Reuters correspondent saw thick smoke billowing over the Old City, near the Grand al-Nuri Mosque, from where Islamic State leader Abu Bakr al-Baghdadi declared a "caliphate" spanning parts of Iraq and Syria.
Heavy exchanges of gunfire and mortar rounds could be heard from the neighbourhoods facing the old city across the Tigris river that bisects Mosul into a western and eastern sides.
The war between Islamic State militants and Iraqi forces is taking a heavy toll on several hundred thousand civilians trapped inside the city, with severely malnourished babies reaching hospitals in government-held areas.
Iraqi Federal Police forces "are engaged in difficult, house-to-house clashes with Daesh fighters inside the Old City", a media officer from these units told Reuters.
Drones are being used to locate and direct air strikes on the militants who are dug in the middle of civilians, he said.
Troops have had the famous centuries-old al-Nuri Mosque leaning minaret in their sights since last month, as capturing it would mark a symbolic victory over the insurgents.
A police spokesman said the troops were closing in on the mosque without indicating the remaining distance.
Their progress has been slow as about 400,000 civilians, or a quarter of Mosul's pre-war population, are trapped in the Old City, according to the United Nations.
As many as half a million are estimated to remain overall in neighbourhoods still under control of the militants in western Mosul, the organisation said in a statement on Monday.
"Civilians in Mosul face incredible, terrifying risks," said the U.N. humanitarian coordinator for Iraq, Lise Grande.
"They are being shot at, there are artillery barrages, families are running out of supplies, medicines are scarce and water is cut-off."
More than 327,000 have fled fighting since the offensive operation started on Oct. 17, with strong air and ground support from a U.S.-led coalition. "Mosul has pushed us to our operational limits," Grande said.
Mosul, the largest city in northern Iraq, was captured by the ultra-hardline Sunni Muslim fighters in mid 2014.
Government forces, including army, police and elite counter terrorism units have taken back most of it, including the half that lies east of the Tigris river.
The militants are now surrounded in the northwestern quarter including the historic Old City, using booby traps, sniper and mortar fire against the assailants.
Police on Sunday reported a toxic gas attack on its troops that caused no deaths. It also said the militants were increasingly using suicide motorbikes attacks.
The narrow alleyways restricts the use of suicide cars by the militants and tanks, armoured personnel carriers and Humvees by the government forces.
The United Nations said last month that 12 people, including women and children, had been treated for possible exposure to chemical weapons agents in Mosul. But Iraq's U.N. ambassador, Mohamed Ali Alhakim, said later there was no evidence for that.
The fighting has killed several thousands among civilians and fighters on both sides, according to aid organisations.
Residents who have managed to escape from the Old City have said there is almost nothing to eat but flour mixed with water and boiled wheat grain. What little food remains is too expensive for most residents to afford, or kept for Islamic State members and their supporters.