Iraqi armed forces launched an operation on Saturday to capture the last Islamic State-held enclave in Mosul, according to a military statement.
The fall of the city would, in effect, mark the end of the Iraqi half of the"caliphate" declared nearly three years ago by Islamic State leader Abu Bakr al-Baghdadi, which also covers parts of Syria.
The enclave includes the Old City centre and three adjacent districts along the western bank of the Tigris river.
The US-backed offensive in Mosul, now in its eighth month, has taken longer than planned as the militants are dug in among civilians.
"The joint forces have began liberating the remaining districts," an Iraqi military statement said.
Another military statement announced the death of two Iraqi colonels during the fighting on Saturday.
Desperate civilians trapped behind Islamic State lines now face a harrowing situation with little food and water, no electricity and limited access to hospitals.
The Iraqi air force dropped leaflets on Friday urging residents to flee but humanitarian groups say they fear for the safety of those trying to escape.
The push inside the Old City coincides with the start of the holy fasting month of Ramadan. The offensive's prime target is the medieval al-Nuri mosque with its landmark leaning minaret, where Islamic State's black flag has been flying since mid-2014.
Iraqi armed forces hope to capture the mosque - where Baghdadi announced the"caliphate" - in the next few days.
Residents in the Old City sounded desperate in telephone interviews over the past few days.
"We're waiting for death at any moment, either by bombing or starving," one said, asking not to be identified."Adults eat one meal a day, either flour or lentil soup."
The United Nations expressed deep concern for the hundreds of thousands of civilians behind Islamic State lines, in a statement on Saturday from the organisation's under-secretary general for humanitarian affairs, Stephen O'Brien.
"Although the UN is not present in the areas where fighting is occurring, we have received very disturbing reports of families being shut inside booby-trapped homes and of children being deliberately targeted by snipers," he said.