Local government officials said the dead include two civilians and four policemen in the attack.
Police officials have cordoned off the area and security force members have surrounded the consulate. However, three hours into the siege, heavy firing was still reported.
The incident occurred after a suicide attacker detonated his explosives at the Pakistani Consulate and opened the way for other attackers to enter.
Meanwhile, Najib Danish, Interior Ministry spokesman confirmed the blast, adding that two more policemen were also wounded in the explosion.
No group has so far claimed responsibility for the attack.
However, investigations are underway.