Two Kenyans, one Ugandan, one Afghan and three Somalis died in the explosion in Garowe town and one American, one Sierra Leonean, one Ugandan, one Kenyan and four Somalis were wounded, police Col Ali Salad told The Associated Press.
Somali President Hassan Sheikh Mohamud called it a direct attack on the future of the country.
"This attack is not just targeted at the United Nations, but in attacking UNICEF, al-Shabab has also attacked Somali children. It is an attack against the future of our country and I condemn it in the strongest possible terms," Mohamud said in a statement.
UNICEF Executive Director Anthony Lake said: "Our colleagues dedicated their lives to working for the children of Somalia. They are not victims. They and those who were wounded are heroes. We mourn their loss and hope for the full recovery of the injured."
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The bomb was apparently planted under a seat and was detonated by remote control, said police official Yusuf Ali.
Garowe resident Jama Hashi said he heard a thunderous blast inside the van, which he said was passing near the offices of the UN's food agency when the bomb went off.
"It's a dark day, but terrorists must know that the blood they shed will not go in vain. We shall deal with them with an iron hand," said Salad, the police commander in the semi-autonomous Puntland state.
UN Secretary-General Ban Ki-moon said at UN headquarters in New York that "the men and women who bring humanitarian action to light are an inspiration to us all.