Following the incident, a heavy contingent of police and Pakistan Army troops reached the site and cordoned off the area, besides sealing all roads leading to the directorate.
Four people have been injured in the firing.
The university was closed due to Eid Milad-un-Nabi (PBUH) holiday.
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Pakistan media Geo news reported that three attackers, with their faces covered, entered the Directorate, located next to the University of Agriculture, and started firing.
Police said at least three militants opened fire at security guards near the gates of the Agriculture Training Institute, injuring one person before making their way inside and targeting student accommodation.
The ISPR said the terrorists were in contact with their handlers in Afghanistan during the attack.
The main Taliban militant group, Tehrik-e-Taliban Pakistan, claimed responsibility saying the place they attacked was housing a secret intelligence office. A security guard was shot and gravely wounded in the attack.
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"We have received six dead bodies and 18 injured, two of them are in critical condition", a spokeswoman for the Hayatabad Medical Complex, Ishrat Bibi, told AFP.
Taliban militants stormed a training institute in Pakistan's northwestern city of Peshawar Friday, as the country marked the birthday of the Prophet Mohammed.
In December 2014, Pakistani Taliban gunmen killed 134 children at Peshawar's Army Public School, one of the single deadliest attacks in the country's history.
The Taliban are fighting to topple the government and install a strict interpretation of Islamic law.
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Peshawar has been the scene of some of the worst violence during the years of an insurgency by the Pakistani Taliban.