Smoke rose from the eastern gate of the palace early Tuesday after more than a half dozen explosions and at least 45 minutes of on-and-off small arms fire.
The Taliban sent a quick text-message statement saying "we brought death to the enemy."
The palace is in a large fortified area of downtown Kabul that also includes the U.S. Embassy and the headquarters for the NATO-led coalition forces.
Reporters gathering for an event with President Hamid Karzai counted at least seven or eight explosions starting about 6:30 a.m.
Police had no immediate comment.