The idea of deploying UN peacekeeping troops to Somalia is "neither realistic nor viable", the UN head has said.
Just 1,600 AU peacekeepers are on the ground in Somalia
Ban Ki-Moon said that because of the security situation, it had not even been possible to send a technical assessment team to Somalia.
His comments come as more than 50 people died in battles in the capital.
A BBC correspondent says Ethiopian forces are engaged in reprisal attacks after two soldiers' bodies were dragged through the streets on Thursday.
Similar scenes were witnessed after Somali militiamen shot down two US Black Hawk helicopters in 1993.
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.
On Friday, Ethiopian soldiers are reported to have fired cannon shells into an area of the south of the city where insurgent militia are thought to be based.
The BBC's Mohammed Olad Hassan in Mogadishu says most of the dead are civilians, killed by the shells fired into markets and residential areas.
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 Mogadishu," Asha Guled said.
'Coalition of the willing'
In August the UN Security Council asked Mr Ban to look at the feasibility of sending UN peacekeepers to Somalia.
Thousands have been fleeing violence in Mogadishu
The African Union (AU) did agree to send 8,000 peacekeepers to Somalia earlier this year but only 1,600 Ugandan troops have actually made it.
The AU only wanted to be there for six months before being replaced by the UN.
Mr Ban suggests the international community could consider other options, including a multi-national force or what he calls a "coalition of the willing".
But 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.
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.