There have been intense clashes on the first day of an offensive by Iraqi forces to retake Mosul's Old City, the last district held by so-called Islamic State.
Special forces and federal police advancing from the west and south were met with mortar fire and car bombs.
The UN says as many as 100,000 civilians are believed to be trapped in the densely populated Old City.
They have been told to leave the area if they can.
The Iraqi military said it was proceeding slowly into the maze of narrow alleyways to minimise civilian casualties.
"The operation now is about street fighting. Air and artillery strikes will be limited because the area is heavily populated and the buildings fragile," Counter Terrorism Service spokesman Sabah al-Numan told al-Hadath TV in Dubai.
IS media outlets said the militants had foiled an advance by Iraqi troops to advance into one neighbourhood and carried out dawn attacks on federal police positions.
Iraqi forces have told the BBC that they do not know how many IS militants are holed up inside the Old City.
About 230 civilians have been killed in western Mosul in the past two weeks, the UN says, some in air strikes and rocket attacks, and others shot dead by IS snipers as they tried to flee.
Residents who have recently escaped from the area have described desperate conditions, with many people running out of food and water.
The beginning of the end - BBC Middle East producer Joan Soley
Different parts of the Iraqi security forces have been creeping closer on all sides. They will not be able to stop now until they have taken back all of the Old City.
Although Iraqi and coalition sources have said there is a "humanitarian corridor" running out of the city along the river, the sheer number of people still inside means there will inevitably be significant casualties - civilians, Iraqi forces and IS fighters.
For the Iraqi government, retaking the Old City is akin to crossing the finish line. The powerful image of IS leader Abu Bakr al-Baghdadi speaking inside its Nuri mosque three years ago is one they are desperate to replace with a picture of "victory" - whether that means Iraqi flags and forces taking selfies at that same spot or blowing the mosque to smithereens.
Afterwards there will still be fighting to be done. The area between Mosul and the Syrian border has to be secured and the town of Hawija, between Baghdad and Mosul, remains under IS control.
Escape from west Mosul - Nafiseh Kohnavard, BBC Persian
We were in contact with three families inside a house right next to an IS sniper position. They had no more food or water. Among them were a woman who was nine months pregnant and elderly people.
They feared that their house would be bombed. A nearby house had already been hit. We passed their address to the US-led coalition, which located it on a grid to avoid striking it. Federal police worked on a plan to get them out.
Overnight the exhausted families told us they were on the point of giving up hope. But they used a nearby explosion and the smoke and dust as cover from the IS sniper and reached safety.
The US-backed offensive to retake Mosul - Iraq's second city - is now in its ninth month. Iraqi forces retook the eastern part of the city in January.
Thousands of Iraqi security forces, Kurdish Peshmerga fighters, Sunni Arab tribesmen and Shia militiamen, assisted by US-led coalition warplanes and military advisers, are involved in the offensive
IS overran Mosul in June 2014, routing the Iraqi army, and shortly afterwards declared it was establishing a caliphate over the territory it then controlled.