Mosul, Iraq's second biggest city, was captured by the ultra-hardline Sunni Muslim fighters in 2014, but government forces have retaken much of it during an operation that has lasted six months.
Officers in Iraq's Federal Police told Reuters that IS shelled government forces with chemical weapons agents in the Urouba and Bab Jadid districts on Saturday.
The attack caused only minor wounds, the force said in a statement, without giving more details.
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The UN 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 UN ambassador, Mohamed Ali Alhakim, said days later there was no evidence for that.
Iraq's Federal Police, one of several forces attacking the militants, said it had made a new push against the group holed up in the Old City, where tanks and heavy vehicles are not able to operate because of its narrow streets.
The front has hardly moved for over a month.
Federal Police forces moved 200 metres deeper into the Old City, getting closer to al-Nuri mosque, a statement said.
The mosque is highly symbolic because it was there that Islamic State leader Abu Bakr al-Baghdadi declared himself head of a self-proclaimed caliphate.
Troops have had the centuries-old mosque with its leaning minaret in their sights since last month.
A captain in the Federal Police said Sunday's advance had started in the early morning with troops fighting the militants house-to-house.
"Daesh (IS) suicide motorcycles now are their favourite weapon inside the Old City," he said.
"We have to watch every single house to avoid attackers on motorcycles packed with explosives."
Iraqi government forces, backed by US advisers, artillery and air support, have cleared the east of Mosul and half of the west and are now focused on the Old City.
Some 400,000 people are trapped in the area and more than 300,000 have fled fighting since the operation started in October, officials say.
Watch: US Defense Secretary responds to civilian casualties in Mosul
