More than 70 people have died and more than 200 have been wounded in battles in Somalia’s capital, Mogadishu.
A BBC correspondent says Ethiopian forces are engaged in reprisal attacks after soldiers’ bodies were dragged through the streets on Thursday.
An adviser to Ethiopia’s leader told the BBC that Ethiopia believed it still had a chance of bringing stability.
His comments come after the UN head said deploying UN peacekeeping troops to Somalia was not realistic or viable.
Fighting between Islamist-led insurgents and elements of the Ethiopian army for control of Mogadishu has intensified during the past two weeks, prompting thousands of citizens to flee the city.
The dragging of mutilated bodies of Ethiopian soldiers through the streets of Mogadishu has provoked a fierce and furious reaction.
As you can see there is nothing they left for us, and most of those who died, died due to injuries they sustained and no medical assistance
Saido Ali Asoble,
On Friday, Ethiopian soldiers were reported to have fired cannon shells into an area of the south of the city where insurgent militia men are thought to be based.
The BBC’s Mohammed Olad Hassan in Mogadishu says most of the dead are civilians, killed by shells fired into markets and residential areas.
Doctors say hospitals are overflowing with badly injured people.
People are trying to escape the violence.
"As you can see there is nothing they left for us, and most of those who died, died due to injuries they sustained and no medical assistance," Saido Ali Asoble told Reuters news agency.
"Ethiopian troops are allowing us to leave our houses to go to safe areas," she said.
Another woman blamed the Ethiopian troops for the problems.
"They killed every person they saw in the area and we have now decided to flee the capital," Asha Guled said.
The insurgents are loyal to the Union of Islamic Courts which was expelled from Somalia after briefly controlling much of central and southern parts of the country.
The transitional government ousted the UIC with the help of Ethiopian troops.
On the question of UN peacekeeping troops, Secretary General Ban Ki-moon said the international community could consider other options, including a multi-national force or what he calls a "coalition of the willing".
The African Union (AU) did agree to send 8,000 peacekeepers to Somalia this year but only 1,600 Ugandan troops have actually made it.
We believe the situation is improving and there is a big chance of stabilising Mogadishu
adviser to Ethiopia’s PM
The AU only wanted to be there for six months before being replaced by the UN.
Diplomats say it is hard to imagine which countries will want to contribute troops given how dangerous and chaotic Somalia is.
Few governments have forgotten the images of US troops being dragged through the streets by Somali militiamen back in 1993.
However, Bereket Simon, special adviser to the Ethiopian prime minister, said Ethiopia was committed to staying in Somalia.
"We believe the situation is improving and there is a big chance of stabilising Mogadishu," he told the BBC’s Focus on Africa programme.
BBC Africa analyst Mary Harpers says that with Mr Ban describing as unviable the idea of deploying a UN force in the country, Ethiopia has little choice but to remain.