In the attack on the compound, two children died, a city administrator said. At least 40 people have been wounded in the blasts.
Police said the full cause of the explosions was yet to be ascertained. Unconfirmed reports said the attack was carried out by a suicide bomber. If confirmed, it would be the fifth such attack on the city in the past 12 months.
No group has come forward yet to say it carried out the assaults.
Khwaja Naseer, of Waqt TV, told Al Jazeera: "It was a very, very horrible scene."
The road outside had been packed with commuters and the blast caused gas-powered vehicles to explode, further hampering rescue efforts.
Hyder said reports were coming through that the attack on the suburb of Model Town had been carried out with a vehicle packed with explosives.
"It was well co-ordinated. The death toll is steadily rising.
"It points to a total failure of the security apparatus that these attacks happened."
The agency specialises in investigating illegal immigration and people smuggling. Chaudhry Manzoor, director of the agency, said 14 employees were among the dead.