Many residents tell CNN the intensity of the fighting and the airstrikes in eastern parts of the city limited their options.
Still, tens of thousands have chosen the escape route.
More than 47,730 people have been displaced because of the ongoing military operations to retake Mosul from ISIS, according to the International Organization for Migration. Roughly 12,800 people have fled since Tuesday, the organization said.
Other residents of Mosul have simply chosen to heed the Iraqi Security Forces instructions to stay in their homes if they feel safe enough inside.
Still others are too scared to leave their homes, because of ISIS' campaign of terror against the civilians.
Witnesses told CNN among the dozens executed this week, more than 30 people were shot in the head for having cell phones. Their bodies were left at various intersections across Mosul as a warning. The bodies are not being removed as residents fear reprisals from ISIS militants, witnesses said.
Here are some of the latest developments in the battle for Mosul:
Bodies hung at intersections
The UN human rights office released a report Friday, confirming that at least 60 civilians have been killed in Mosul this week, and reported new details of alleged atrocities by ISIS fighters.
On Wednesday evening, ISIS reportedly killed 20 civilians at the Ghabat military base in northern Mosul on charges of leaking information, the UN body said. "Their bodies were also hung at various intersections in Mosul, with notes stating: 'decision of execution' and 'used cell phones to leak information to the ISF.' "
On Tuesday, ISIS shot and killed 40 civilians in Mosul after accusing them of "treason and collaboration" with Iraqi security forces, according to a report by the Office of the UN High Commissioner for Refugees, or UNHCR.
"The victims were dressed in orange clothes marked in red with the words: 'traitors and agents of the ISF.' Their bodies were then hung on electrical poles in several areas in Mosul city," the report said.
Teens trained to fight for ISIS
Local ISIS commanders have started fleeing in some neighborhoods, residents said, leaving behind trained teenage ISIS combatants to fight Iraqi forces.
Mosul residents said they fear these young fighters as much, if not more, than other ISIS militants because they have been brainwashed, have no fear and have a great amount of zealotry after being indoctrinated and trained for two years.
The UNHCR report said ISIS had "deployed what it calls the 'sons of the caliphate' in the alleys of the old town of Mosul, wearing explosive belts. We are concerned that these may be teenagers and young boys."
ISIS posted video footage Wednesday, "showing four children, believed to be between 10 and 14 years old, shooting to death four people for spying for the ISF and the Peshmerga," the report said, referring to Iraqi and Kurdish forces.
UN human rights chief Zeid Ra'ad Al Hussein cited "heartbreaking images" of ISIS forcing children to carry out executions and reports of women being "redistributed" among ISIS fighters, as evidence of the "numbing and intolerable" suffering of civilians in Mosul and other ISIS-held areas.
He called on Iraqi authorities to ensure the perpetrators of such abuses are dealt with according to the rule of law so as to limit revenge attacks and help communities rebuild.
Senior ISIS leader killed
In another development, Mahmoud Shukri al Nuaimi, a senior ISIS commander, has been killed in the battle for Mosul, the terror group's last major stronghold in Iraq, Iraqi military intelligence sources tell CNN.
Al Nuaimi, also is known as Sheikh Faris, was killed Tuesday in an Iraqi-led coalition airstrike in western Mosul, the sources said.
ISIS confirmed his death in a video montage, referring to him as "the martyr of the battle."
The Iraqi sources told CNN that Nuaimi was formerly a high-ranking intelligence officer in Saddam Hussein's intelligence services.
In Mosul's east, residents said ISIS militants were forcing them from their homes, either to booby trap the houses or to take them over as fighting positions. Militants have reportedly left barrels of crude oil at major intersections, ready to be set afire to hamper Iraqi advances.
ISIS has also used white flags to disguise suicide car bombs in Mosul, according to Saban Al Numan, an Iraqi counterterrorism official.
The battle for Mosul is difficult, slow and complicated, Numan said.
Iraqi Prime Minister Haider al-Abadi vowed victory last month at the start of the long-awaited offensive on Mosul, but he warned the effort could take time.
ISIS, an agile enemy, has been preparing its defenses for two years
. It takes advantage of the terrain, a network of tunnels and booby-trapped buildings, to great effect.
US military officials estimate some 3,000 to 5,000 ISIS fighters are in Mosul. An additional 1,500 to 2,000 fighters may be waiting outside the city limits.