The first rocket caused some damage inside the heavily fortified palace compound, while the second hit the capital's police headquarters, but caused no casualties, reports Sky News.
Officials said the militants targeted residential areas and held hostages.
ISI chief Faiz Hameed coerced the Taliban to announce an interim government guaranteed to preserve Pakistan's control over the levers of power in Kabul, observes Ambassador M K Bhadrakumar.
Afghanistan President Ashraf Ghani has delayed his visit to India by a few hours.
The Taliban have the ISIS in its crosshairs. The Taliban has shown the skill to assimilate extremist elements if they are reconcilable as well as the ruthlessness to eliminate troublemakers, observes Ambassador M K Bhadrakumar
An audio message has been released in Pushto, circulated by Taliban commanders, where Akhundzada said, "Taliban will never bow their heads and will not agree to peace talks," reports Dawn.
Their leaders in the provinces, which have been under the control of Taliban commanders for several months now, speak the language of the bigot. Women are known to have been abducted and enslaved. Several young girls have simply disappeared.
In a major crackdown to eliminate the terrorists' sanctuaries, Afghanistan has carried out three air strikes within a week in Kunar province, bordering Pakistan, inflicting heavy casualties on Lashkar-e-Tayiba terror group.
Trump had a hastily-arranged bilateral meeting with Afghan President Ashraf Ghani
As many as 10 Taliban fighters, dressed in Afghan army uniforms and driving military vehicles, talked their way onto the base and opened fire on soldiers.
The Taliban's official spokesman, Abdulqahar Balkhi, claimed responsiblity for the attack on Twitter.
The latest militant assault on the Afghan capital comes as the Taliban intensify their nationwide offensive against the US-backed government in Kabul.
Taliban's reclusive leader Mullah Muhammad Omar is alive and hiding in the Pakistani city of Karachi, a top Afghan intelligence official has said, echoing a similar assessment by Western intelligence officials.
The Taliban helmed attack on the Afghan parliament on Monday, ended with all six gunmen killed, the interior ministry said.