ISIS claimed responsibility for the attack, the first to hit the capital since the start of the new year.
'Iran wants to play the same game in Afghanistan that it played under the name of ISIS in Iraq and Syria,' the former militant commander said.
The year was one of the bloodiest on record for Afghanistan, as militants targeted civilians with suicide attacks and mines.
The defeat of ISIS in Iraq and Syria will bring an end to the group in Afghanistan, Pakistan and Central Asia -- where security forces are ready to deal with any new challenges, analysts say.
The militants are also forcing young children in the province to undergo terrorist training, including to serve as suicide bombers, officials and local residents say.
Militants from both sides have been killed in the ongoing battles in Nangarhar and Laghman provinces.
Seeking to hide the crimes they have committed, ISIS and the Taliban have increased attacks against journalists and the media.
Military operations and a lack of public support have halted the expansion of ISIS in Afghanistan and Pakistan, say analysts.
Afghanistan and Pakistan are among 41 countries that have joined the 'pan-Islamic unified front' against violent extremism.