A source from the presidential palace, who did not want to be identified because he was not authorised to talk to the media, said one of the rockets hit a tree inside the palace's compound, but caused no casualties.
It was rare attack in Kabul city, which is guarded by thousands of Afghan and international forces just two days before the nationwide presidential elections.
Rebels have fired rockets into Kabul twice this month, but there were no casualties in either instance.
Taliban also fired rockets at Nangarhar province's airport Monday night, wounding at least ten civilians, Ajmal Pardes, head of the provincial public health department said.
Ahmad Zia Abdulzai, spokesman for the provincial governor confirmed the attack, but said there were no casualties among government forces in the province or damage to the airfield's premises.
In an apparent attempt to scare the Afghans and prevent them from taking part in the election, which is the second direct vote for the president in Afghanistan's recent history, Taliban militants have intensified their assaults in the past two weeks.
A Taliban suicide bomber attacked NATO's military headquarters in Kabul Saturday, killing seven Afghan civilians and wounding more than 90 others including several NATO soldiers.