The extremist leader has been linked to a plot to attack Times Square in New York City.
The demand comes after two major Taliban attacks in Kabul that left 150 civilians dead.
Militants kidnapped the professors in Kabul in an August raid.
The attack brought the death toll from two days of violence to 25 after Monday's double bombing in the city.
Haibatullah Akhunzada is to lead the group after a U.S. drone strike killed the former chief.
President says Mansour's death in airstrike an "important milestone" in bringing peace to Afghanistan.
Mullah Akhtar Muhammad Mansour is hoping to end months of infighting.
Militants breached the heavily-fortified airport, which serves as a base for Afghan and Nato troops.
The clashes follow days of confusion over the fate of Mullah Mansour.
Taliban Leader Mullah Akhtar Mansour 'Died of Injuries', Says Afghan Spokesman
The Taliban revealed April 23, 2013 as the date of his death.
Hamza bin Laden praises lone wolf attacks like the Boston bombing and the Fort Hood massacre.
The suspects were found to have provided safe haven and supplies for the attackers.
The explosion is the latest in a series of suicide attacks in Kabul following a change in Taliban leadership.
The bombings were the first in Kabul since Mullah Akhtar Mansour took charge of the Taliban last week.
Truck bomb kills at least six people in Logar province, south of Kabul.
Peace talks between the Afghan government and the Taliban were suspended on Friday at the request of the Taliban.
ISIS will challenge the new Taliban ruler's religious legitimacy by claiming to be more pious and religiously pure.
Several senior Taliban figures walked out in protest after Mullah Akhtar Mohammad Mansour was named as the Islamist militant group's new head.
Not long before word spread of the Taliban leader's passing, reporter Sami Yousafzai received an unexpected phone call.
The Taliban supreme leader died two years ago in a Pakistani hospital, a spokesman said.
What relationship the Islamic State will have with the Taliban in the country remains to be seen.