The rubble-strewn city had been relatively peaceful this week during tentative UN peace talks in Djibouti between the interim government and opposition figures based in Eritrea.
But the calm was shattered on Friday when at least eight people were killed, and locals said eight more died on Saturday.
Witness Ismail Hussain said Ethiopian troops supporting the government shot dead three students in Waberi district.
"They were in school uniform but carried no books. I think the soldiers suspected them (of being insurgents)," he said.
Elsewhere, residents said five people, including two government troops, died overnight in a fierce battle in northern Mogadishu's Industrial Area.
"Government forces came early this morning and took two of the dead, who were in uniform. The other three wore ordinary clothes and are unidentified," local resident Fatuma Osman said.
In Qashadeere, a town in central Somalia, residents said another government soldier was killed by unknown assailants.
There was little progress at this week's discussions in Djibouti, with opposition officials demanding Ethiopian troops leave Somalia before face-to-face negotiations could take place.
The International Committee of the Red Cross has warned that it sees no immediate improvement in the country's humanitarian crisis, which aid workers say may be the worst in Africa.
At least a million people have been uprooted by fighting between the government and Islamist insurgents since early last year, and their plight has been worsened by record food prices, hyper-inflation and drought.