The area remains under lockdown after an intense gun battle took place near the defence ministry and the nearby CIA office.
Journalists were forced to flee as gunfire erupted shortly before a press conference was due to be held.
A series of explosions and gunfire were heard outside the palace, one of the most heavily guarded areas in the Afghan capital.
Police say that all the attackers have now been killed.
The attack comes just days after Karzai said he will not enter peace talks with the Taliban unless they are Afghan-led.