The attack took place on Sunday evening on a busy road leading to the government district, outside a popular cafe.
"It shows the desperation of al Shebab because they are only hurting innocent civilians," Mohamud said in a statement, updating an initial toll after the blast of four.
In addition, 18 others were wounded, some of them seriously, Mohamud added.
Witnesses said the blast could be heard several streets away.
"I saw charred bodies, I don't know who was targeted but the explosion was very strong and the site was destroyed," said witness Ahmed Yusuf.
The al Qaeda-linked Shebab insurgents have not claimed responsibility for the attack, but the fighters have stepped up guerrilla attacks in the capital and elsewhere in the country after being chased from key cities by African Union-led troops.
The bombing also came a week after the Shebab were pushed out of Barawe, the last major port in Somalia that was held by the group and a key source of revenue for the Islamist militia.
Somalia has been riven by civil war since 1991.
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