The armed groups, made up of the remnants of the Union of Islamic Courts (UIC) movement that was ousted from the city last year, as well as a number of clan militias fighting alongside them, have fired mortars from inside residential areas.
Ethiopian troops have used heavy artillery to shell the fighters' positions inside those areas.
"The situation is Somalia has gone from bad to worse after the intervention of Ethiopian troops"
Abed, Kumasi, Ghana
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However, civilians caught in the crossfire have been the main victims. Hospitals have been overwhelmed, but most victims have been unable to seek any kind of help because of the ongoing clashes.
Doctors were also trapped in their homes by the violence and thousands of people have fled Mogadishu in recent days.
Corpses remained on the streets as ongoing fighting and mortar fire made it difficult to retrieve bodies or tally the dead. An Agence France Presse (AFP) correspondent on Sunday saw the bodies of at least six civilians lying in the street.
Residents said hundreds were believed to have been killed across the city of one million people.
AFP quoted Ibrahim Duale, a resident in the southern Ali Kamin area, as saying: "We don't know where to go. We are trapped in our houses and dead bodies are lying in the street."
"There is no chance of taking the wounded and dead people because of the heavy artillery and anti-aircraft weapons."
The fighting shattered a brief and shaky truce between the Ethiopians and leaders of the city's dominant clan, the Hawiye.
Security sources said African Union (AU) officials were pushing for more talks between the two sides to reinstate that ceasefire, but were facing massive mutual mistrust.
Talking to Shabelle, an independent Somali broadcaster, a Hawiye spokesman called on the United Nations, United States, European Union and Arab League to urge Ethiopia to stop attacking.
|One resident said the city was being |
"shelled indiscriminately" [AFP]
"What is happening in the city is total carnage against the civilians," he was quoted as saying on their Web site on Sunday.
While Addis Ababa seems determined to crush remaining fighters, some analysts say the offensive could have the opposite effect of turning Somalis further against their predominantly Christian neighbour, or drawing in foreign Muslim fighters.
Despite the fighting, Somalia's interim government remains confident a reconciliation meeting of elders, politicians and former warlords planned for April 16 will go ahead in the city.
The mandate for the administration, which is the 14th attempt to restore central rule in Somalia since 1991, runs out in 2009, after which, in theory, there should be elections.
A Ugandan soldier was killed by artillery in Mogadishu in the first death reported by African peacekeepers in the Somali capital, a spokesman said on Sunday.
Major Felix Kulayigye, a Ugandan military spokesman, told Reuters: "Our troops were guarding the presidential compound on Saturday when it was struck by mortars. One of our soldiers was killed."
The AU has sent 1,200 Ugandan troops to help the government, but they have been attacked by the armed groups. Other African nations are baulking at sending more peacekeepers to boost the AU force to its planned strength of 8,000.