A rocket has hit the presidential palace in the center of Afghan capital, Kabul and a second has struck the city's police headquarters, a police source says, reported Press TV.
The assaults on Tuesday morning caused some damage but no one was reportedly wounded in either attacks.
Meanwhile, Taliban spokesman Zabihullah Mujahid claimed the militants had fired four rockets at the capital, but he declined to mention more details.
The attacks came just 48 hours before the presidential election in the country.
Taliban have vowed to interrupt the election and they have already fired rockets at the Afghan capital twice this month.
On Saturday, a suicide car bomb exploded outside the NATO military headquarters in the Afghan capital Kabul near the US embassy, killing seven people and injuring scores.