One of the targets of the new push is Faruq Street, which runs near the Great Mosque of al-Nuri where Daesh chief Abu Bakr al-Baghdadi made his only known public appearance after the terrorists seized Mosul in 2014.
Iraqi forces have been operating in the Old City area for several weeks, but they have faced tough resistance and progress has been slow.
Government troops and volunteer Hashd al-Sha’abi forces drove Daesh militants from the eastern part of Mosul, Iraq’s second-largest city, early this year. The fight has now moved to Mosul’s densely populated western neighborhoods.
On Monday, the commander of the federal police Lieutenant General Raed Shakir Jawdat said his troops and Rapid Response Division units began to advance on the southwestern axis of the Old City.
The government launched the operation to retake Mosul in October. Daesh overran large areas north and west of Baghdad in 2014, but Iraqi forces have since retaken much of the territory they lost.
Prime Minister al-Abadi told Fox News Sunday that Iraq is defeating Daesh "militarily" but that the terror group would continue to exist until it is eradicated in Syria and elsewhere in the Middle East.
“As a terrorist organization, they will try. So that's where we need the efforts of others. Flush them out of Syria and other places,” he said.
The United Nations says 400,000 people are "trapped" in central Mosul under siege-like conditions as Iraqi forces battle Daesh for the city's west.
The city is reeling from US aerial attacks on March 17 which reportedly killed more than 200 people.
On Saturday, the US acknowledged that it had carried out a strike on a location in west Mosul where civilians were reportedly killed but Iraqi officials referred to more than one day of strikes.
The United Nations has said it was “stunned by the horrendous loss of life” in the attacks. Iran’s top security official has called the airstrikes a “war crime” which should be urgently addressed in a court of justice.
The Iraqi Observatory for Human Rights said on Sunday that since the campaign against western Mosul began on Feb. 19, nearly 700 civilians have been killed in airstrikes which are mainly carried out by the US.
In one incident, nearly 40 people were killed in a US airstrike in western al-Jawsaq neighborhood after Daesh militants used the residents as human shields, the group said.