"The first explosion took place at 6.20 a.m. and it was followed by another blast at 6.32 a.m.," an official said.
"The first blast targeted a government bus carrying security personnel in Kart-e-Char locality in western Kabul," Xinhua quoted the official as saying.
Details about the second blast are not known yet.
The attacks came a day after the country and the US inked the Bilateral Security Agreement (BSA) to allow limited number of troops to remain in Afghanistan after the 2014 pullout of NATO-led troops in the country.
"I think the attack is a Taliban response to the signing of the BSA with the United States," the official added.