AFP quoted Ali Musa Mohamed, a medic with an ambulance service, as saying that they had collected at least 13 wounded civilians.
An AFP reporter earlier heard an exchange of mortar and artillery fire in areas close to the presidential palace.
Residents emerged from homes to seek food, or join 49,000 others who have fled Mogadishu in the past two weeks.
"Large number of families started fleeing today from new districts and this will deepen the already worsening humanitarian situation," Ali Yasin Gedi, vice-chairman of Elman Peace and Human Rights Organisation, told the Reuters news agency.
The deaths on Saturday come on top of the nearly 45 lives lost the previous day when government forces launched a pre-dawn offensive against the two main anti-government groups.
The aim was to drive al-Shabab and Hizbul Islam - who have pledged to topple the government of President Sheikh Sharif Sheikh Ahmed - from their Mogadishu strongholds.
Witnesses said at least four members of al-Shabab and a journalist were among the victims of Friday's clashes.
Farhan Mahdi, a Somali military spokesman, said: "This is a large military offensive against violent people.
"The government will sweep them out of the capital and the fighting will continue until that happens."
The government claimed that it had regained control of three areas of Mogadishu - Tarbunka, Bakara and Howlwadag - as a result of the offensive.
But al-Shabab rejected the claims.
"The enemy of Allah attacked our positions this morning and our fighters are defending themselves," Sheikh Ali Mahmoud Rage, a spokesman for al-Shabab, said.
"They have not not taken any positions from us."
And Sheikh Hassan Dahir Aweys, al-Shabab's leader, said his forces were still in control.
"It is clear that they have launched an attack on our positions in Mogadishu and also some of the ministers of government said that they have attacked forces on our positions," he said.
"But we won both attacks. We won over their aggression on our forces and we will continue to do so for the will of God."