The Ethiopian troops have also been accused of looting several hospitals.
In a statement, John Holmes, the UN humanitarian chief, called for greater protection of civilians.
"He also strongly condemned the brutal killings that occurred on 20 April at Al Hidaaya mosque in Heliwaa district of Mogadishu, where women and children were present," said a statement from his New York office.
Holmes's statement said heavy artillery was used in residential areas during recent clashes. "Combatants appear to have little regard for the safety of civilians in Mogadishu, where residents have been traumatised by years of violence."
Civilians have borne the brunt of the Somali conflict with a local rights group saying that about 6,500 people were killed last year.
Thousands of Ethiopian troops patrol Mogadishu, propping up the weak Somali government during an increasingly deadly insurgency.