Information Minister Farhan Ali Mohamud announced the death of National Security Minister Omar Hashi Aden but declined to give any other details.
Somalia's president accused al-Qaida of being behind the bombing, which he said also killed a senior Somali diplomat.
"It was an act of terrorism and it is part of the terrorist attack on our people," Sheik Sharif Sheik Ahmed told journalists in the capital. "Al-Qaida is attacking us."
Experts have expressed fears that foreign Islamic militants could use Somalia as a base for terror in the region.
Al-Shabab, an extremist Islamist group in Somalia, is considered by the U.S. State Department to be a terrorist organization with links to al-Qaida. Al-Shabab has denied the links.
The United States accuses al-Shabab of harboring al-Qaida-linked terrorists who allegedly blew up U.S. Embassies in Kenya and Tanzania in 1998. The United States has attempted to kill suspected al-Qaida members in Somalia several times with airstrikes.
Somalia has not had an effective government for 18 years after warlords overthrew a longtime dictator and plunged the country into anarchy and chaos. The lawlessness has also allowed piracy to thrive off the country's coast, making Somalia the world's worst piracy hotspot.
Islamic insurgents have been trying to topple Somalia's weak, Western-backed government for more than two years. There was a surge of violence in May, during which almost 200 people were killed. The U.N. says the conflict has displaced more than 122,000 people.
At least 17 people were killed in overnight battles between Islamic insurgents and government forces in Mogadishu, witnesses said Thursday.
Information Minister Farhan Ali Mohamed denied the government targeted residential areas, adding government forces were only defending themselves.
An insurgent spokesman, Hassan Mahdi, said his side did not attack any government positions but were defending themselves. Mahdi said once the insurgents repulsed the government forces then the government side started shelling residential areas.
Neither spokesman gave any casualty figures. Mogadishu does not have any clearly defined battlegrounds and both sides' forces are located close to residential areas.
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