The hilltop presidential palace, Villa Somalia, and the coastal city's defence headquarters were among the targets hit on Tuesday.
Hospital sources said dozens of people were wounded.
"They showered us with rockets and a mortar also hit the compound. Luckily no one was hurt," said a government soldier who was in Villa Somalia during the attack but declined to be named for fear of reprisal.
"Our troops and those from our ally Ethiopia were forced to fire heavy artillery," he told Reuters. "We had to retaliate. These elements are being paid to cause all this destruction."
A woman living nearby said several people were wounded in the surrounding streets, and a Reuters TV cameraman saw five bodies in a western neighbourhood also hit by mortar rounds.
Insurgents
A spate of near-daily rocket and mortar strikes have challenged the weak interim government's bid to impose security and let Ethiopian troops who helped it oust the courts go home.
Salad Ali Jelle, deputy defence minister, said two civilians were killed in the attack on the defence headquarters, and he also accused remnants of the courts union of paying the assailants.
"The insurgents are paying $100 a day to whoever fires rockets and mortars at the government and people," he said.
But Jelle said a 24-hour rapid response paramilitary unit that was unveiled on Monday would soon show results in its fight to stop the wave of guerrilla attacks.
"The plan is to expand our control in the city so the extremists are no longer safe anywhere... We intend to make it very hard for them to continue operating," he said.
With Ethiopian military help, government troops have boosted patrols and set up more checkpoints.
The attacks underscore the huge challenge facing the interim government of Abdullahi Yusuf, the president, as it tries to tame a nation in anarchy since Mohamed Siad Barre, the former president, was ousted in 1991.
His administration says it is doing its best to police one of the world's most dangerous cities with little help.
