Kabul criminal investigation police chief says first attacker hit a bus with Afghan National Army officers, killing seven.
The attack took place near the town of Afgoye, some 30 kilometres northwest from the capital Mogadishu.
The bombing was followed by clashes with militants who tried to overtake the town.
Worst bombing since 2001; over 40 injured.
A suicide bomber detonated his explosives-laden vehicle alongside the armored car of Mohammed Masoom Stanikzai.
Six soldiers and a civilian were killed in three separate bombings in Pakistan, including twin blasts in Islamabad.
Iraq has been hit by a year-long surge in bloodshed driven principally by widespread discontent among its Sunni Arab minority.
The bus was carrying 33 South Korean tourists and two Egyptians when the bomber detonated his explosives.
Day after attack on troops, Taliban claim responsibility for another bombing.
The attack comes a day after a Taliban bombing that killed at least 20 troops.
Hashmat Stanekzai, a spokesman for Kabul police, said an operation to clear the building was under way.
The Pakistani Taliban used around 200 kg of explosives for the suicide attack on Aslam, known for his crackdown on the outlawed militant group.
Hassan and the bomber died but no other students or staff were hurt, police said.
Second deadly bombing in 3 days as country prepares to host Winter Olympics in 40 days time.
Suicide bomber rammed an explosives-packed vehicle into a security checkpoint in Benghazi.