The Iraqi military says its forces had success against Islamic State (IS) forces south of Mosul and also recaptured districts within the city.
Military officials said on November 4 that Iraqi troops had taken back six districts from IS fighters in eastern Mosul.
Iraq's Counterterrorism Service said the neighborhoods of Malayin, Samah, Khadra, Karkukli, Quds, and Karamah were under Iraqi control.
Reports said the advancing troops were coming up against fierce opposition and that IS militants were firing mortars, bombs, automatic weapons, and rockets.
At one point Iraqi troops had to pull back from Karamah after IS militants unleashed a hail of bombs and gunfire.
The fighting on November 4 was the most intense urban combat in Mosul since government and Kurdish forces launched an offensive on October 17 to drive out the militants, AP reported.
There are an estimated 3,000 to 5,000 IS fighters scattered in different parts of Mosul.
Meanwhile, Iraqi security forces advanced along the Tigris River and entered the Hammam al-Alil district, just 20 kilometers from Mosul.
IS fighters retreating ahead of the advance and going north to Mosul have forced thousands of villagers and people from towns such as Hammam al-Alil to travel with them to protect against air strikes, Reuters reported.
The UN said IS militants took some 1,600 abducted civilians from Hammam al-Alil to Tal Afar, west of Mosul, earlier this week, and took another 150 families from Tal Afar to Mosul the next day.
Residents were told to give IS fighters their children, especially boys above the age of nine, in what was seen as a drive to recruit children as soldiers, UN human rights spokeswoman Ravina Shamdasani said.
The reported advances toward and within Mosul come one day after IS leader Abu Bakr al-Baghdadi released an audio recording in which he called on the militants not to retreat from Mosul.
The territory taken by the Iraqi forces thus far still amounts to just a tiny fraction of the sprawling city of some 1.5 million inhabitants.
There has also been an exodus of civilians from villages such as Gogjali and Bazwaya in recent days, with the UN refugee agency saying some 3,000 displaced persons have arrived at a newly opened camp.
Umm Ali could not hold back tears when she spoke of her constant fear the jihadists would take her sons.
"They kept coming to our home," she said. "Sometimes they'd knock on the door at 10 p.m. They took our car, saying, 'This is the land of the caliphate, it belongs to us.'"
Many civilians seeking refuge in the Kurdish-controlled villages east of the city also told stories of IS brutality since the Sunni extremist group took control of Mosul and other areas of northern and western Iraq in 2014.