The bombing took place in a high security zone that houses several government offices, including the headquarters of Afghanistan's primary intelligence agency - the National Directorate of Security (NDS).
Interior Ministry spokesperson Nasrat Rahimi said the blast that took place at 10.10 a.m. in Shashdarak area of Kabul killed 10 civil and wounded 42 others. Some 12 private vehicles were also destroyed in the powerful explosion.
A NATO statement said that two members of Resolute Support mission were killed in the Kabul bombing, according to Efe news.
"One service member was from Romania The second service member was from the US," the statement said.
The Taliban insurgent group claimed responsibility for the Kabul attack, saying the suicide bombing targeted a convoy of "foreign invaders" going to the NDS office.
Its spokesperson Zabihullah Mujahid tweeted that three Land Cruisers were "completely damaged" in the attack that killed "12 foreign invaders and eight NDS soldiers".
Afghanistan President Ashraf Ghani "strongly" condemned what he called a "cowardly attack on civil by the Taliban".
"They have shamelessly claimed responsibility and are celebrating the deaths of innocent lives," he said.
The explosion comes as the US and the Taliban are believed to have finalized in principle an agreement for peace in Afghanistan after a year of negotiations to end the 18-year old war.
The attack follows Monday's Taliban suicide bombing when a tractor laden with explosives was detonated near a heavily-guarded residential complex in the Afghan capital that mostly houses foreigners. At least 16 civil and five attackers were killed and nearly 119 injured.
The Taliban called the area a "nest of foreign invaders".
( With inputs from IANS )