Civilians threatened
Twenty people were killed on Saturday in the Al Barakah residential and market area when mortars hit the area, witnesses told Reuters.
Ethiopian forces had earlier fired shells from the presidential palace in southern Mogadishu at Islamic courts fighters, sparking retaliatory gunfire.
Ethiopian army units also fought battles in the northern Fagah district and areas near the main Bakarah market.
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"The situation is Somalia has gone from bad to worse after the intervention of Ethiopian troops"
Abed, Kumasi, Ghana
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"The Ethiopian forces are shelling Bakara market, mortars are landing everywhere and at this moment, we do not know what to do," said Hashim Ali Mohamed, who lives in southern Mogadishu.
The UN has warned of a humanitarian crisis as the violence continues, with widespread outbreaks of cholera and diarrhoea being reported.
About 1,500 African Union (AU) peacekeepers from Uganda deployed in Mogadishu since early March have failed to bring control.
The Ugandans are an advance contingent of about 8,000 peacekeepers the AU has pledged to Somalia to help Abdullahi Yusuf Ahmed, Somalia's president, restore full control of the country.
Ban Ki-moon, the UN secretary-general, called on Friday for world support for African peacekeepers but said pursuing military solutions in Mogadishu was likely to be "counter-productive".