The Islamic courts, which still has support in Mogadishu, has vowed to wage an Iraq-style fighter operation, though it was immediately unclear why residential areas were targeted.
In one incident, Jamae Nour Ahmed, Al Jazeera's correspondent in Mogadisu, said, two children were killed and several others injured when mortar shells landed on their home in southern Mogadishu.
Another child was killed and six others were wounded when two shells landed in the Bolo-Hobi suburb.
Sadiya Dahir Nur, a mother of six, said: "A mortar hit our house, killing my 14-year-old daughter who had returned from school."
Another three mortars were aimed at Mogadishu's airport, but no casualty or damage was reported there, Mohamed Ahmed Mohamed, airport manager, said.
In another incident, a woman was killed and several others were injured when unidentified assailants fired rocket-propelled grenades at Kaah hotel, in northern Mogadishu, Al Jazeera's correspondent said, adding that several people were also injured in a mortar attack on a livestock market.
Kaah is the venue of an ongoing political reconciliation meeting in the Somali capital.
Another hotel, the Global, was hit by a rocket late on Friday, just hours after a masked man at a pro-Islamist courts rally said that Ethiopian soldiers would be attacked in their hotels. No one was injured in the incident.
The man, who gave his name only as Abdirisaq, claimed he was speaking on behalf of a group called the Popular Resistance Movement in the Land of the Two Migrations.
He said the group was responsible for attacks on Somali government buildings and Ethiopian troops in Mogadishu.
The same group claimed responsibility for the attack at the Global hotel, with a message on Saturday on the official website of the Islamic courts, saying it had targeted Ethiopian generals staying there.
Before ousting the Islamic courts from Mogadishu, and prompting its supporters to flee over the border to neighbouring Kenya, the government was confined to Baidoa.
Also on Saturday, Kenya handed over about 20 people suspected of having fought with or been linked to the Islamic courts to the Somali authorities, a British diplomat and a Kenyan police officer said, both speaking on condition of anonymity.