According to local officials, the first blast happened after a suicide bomber detonated his explosives near Afghan National Police convoy in Company area at around 12:00PM.
A security source who spoke on condition of anonymity said the second attack targeted a bus carrying police cadets as they were on their way from the neighboring Maidan Wardak province to Kabul city.
Abdul Rahman Rahimi, Kabul police commander at the scene also confirmed the two deadly explosion. But he did not specify the exact number of casualties.
Meanwhile, Sediq Sediqi, spokesman for the Ministry of Internal Affairs wrote in his Twitter account that the details of the attack is ongoing and will be presented to the public later.
However, a number of media have reported so far that at least 27 police officers were killed and over 40 others were injured in the attacks.
Armed Taliban group claimed responsibility for the blasts.
Zabihullah Mujahid, a Taliban spokesman in a statement said about 150 police officers and teachers killed and wounded.