Ali Yasin Sheik Fadhaa, vice chairman of the independent Elman Human Rights Organisation, reported Thursday's death toll and said that 26 people had been killed in total over the last two days.
"Thousands have also evacuated in this period because fighting has spread to new districts," he said.
Years of conflict in Somalia have killed tens of thousands of people, displaced millions more, and created one of the world's worst aid crises.
Fighters, many from the armed al-Shabab group, are known to hide among civilians.
Mogadishu residents also accuse African Union peacekeepers, in Somalia to back the government, of shelling the fighters strongholds, while
But Barigye Ba-Hoku, an AU spokesman, said: "We are neither involved in fighting nor shelling ... The opposition blames shelling on us as an excuse to attack our bases."
Aid organisations warned on Thursday that Somalia's worst fighting in months was aggravating an already dire humanitarian emergency in the Horn of Africa nation.
The UN said that one and half million Somalis could die from hunger in the next six months and its officials have suggested they are willing to talk to al-Shabab fighters to secure aid deliveries.