Haroon Zarghhon claimed responsibility for Tuesday's attack near Kabul airport in an email to The Associated Press. He said the attack was carried out by a 22-year-old woman named Fatima.
He is with the group called Hezb-e-Islami led by former warlord Gulbuddin Hekmatyar.
Police say a suicide bomber rammed a small sedan heavily laden with explosives into a mini-bus believed to be carrying foreign aviation workers to the airport at dawn.