The second explosion happened at the scene of the first explosion about 20 minutes later after emergency personnel and journalists arrived in the area.
The attacks came just a week after a blast at a voter registration centre killed 60 people, in the wake of warnings by security officials against the risk of increasing attacks ahead of parliamentary elections planned in October.
Monday’s first explosion in the Shashdarak area close to buildings of the NDS intelligence service was followed by one outside the headquarters of the ministry of urban development and housing, just as people were entering the government office.
A Kabul police spokesman confirmed the blast and said it might have been caused by a suicide attack, but there was no confirmation and no immediate claim of responsibility.
Taliban militants, fighting to restore their version of strict Islamic law to Afghanistan, announced their usual spring offensive last week and there has been heavy fighting in several areas of the country since.
Hundreds of people have been killed and wounded in a series of high-profile attacks in Kabul since the beginning of the year, despite President Ashraf Ghani’s offer in February for peace talks “without preconditions”.