The attack underscored how despite efforts by the Afghan authorities to improve security, militants in this country are still able to stage large-scale and complex attacks, including in the country's capital, Kabul.
The dead included seven students and one teacher, according to Afghan authorities. Three police officers and two security guards were also killed, the interior ministry said.
No group has yet claimed responsibility for the assault but suspicions are pointing to the Taliban. The group's spokesman, Zabihullah Mujahid, would only tell the media that the Taliban are "investigating."
Ghani spoke by telephone with Pakistan's army chief, Raheel Sharif, and demanded "serious action," his office said. Pakistan's foreign ministry "strongly condemned" the attack.
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Ghani's statement also raised the death toll to 13, saying that a teacher, identified on social media by the as Naqib Khpolwak, a graduate of Stanford Law School and a doctoral candidate at Oxford University, was also among those killed.
"Most of the dead were killed by gunshots near the windows of their classrooms," said Sediq Sediqqi, the spokesman for the Ministry of Interior. The ministry said 36 people were wounded, including nine police officers.
The blast breached the security walls and allowed two other "terrorists," beside the driver of the vehicle, to enter the campus, Sediqqi said.
They were armed with grenades and automatic weapons. The siege of the university lasted almost nine hours, before police killed the two assailants around 3.30 am, he added.
More than 200 people, mostly students who had been trapped in university buildings were rescued by special police units.