In a video message, Taliban leader Umar Mansoor condemned the prevailing educational system which he alleged was foundation of the political, justice, defence and democratic institutions.
"We have started the process of attacking educational institutions," he said in about 10-minute video posted on Facebook.
The video is in Pushto with Urdu sub-titles, showing Mansoor flanked by armed men. With his long flowing beard, the rebel spoke with confidence as he denounced Pakistan's rulers.
"Pakistan's entire system is that of infidels... we will change it. We will continue to attack schools, colleges and universities across Pakistan as these are the foundations that produce apostates. We will target and demolish the foundations," he said.
Mansoor said that instead of targeting professional soldiers, "we will target the nurseries that produce these people".
The location of the shooting of video is not known but most probably it was produced in Afghanistan where most of Pakistani militants live after being expelled from the country through military operations.
The university attack killed 21 people, mostly students, while four attackers were gunned by the security forces.