"I have seen the body of an Ethiopian soldier at al-Baraka junction. Another soldier was wounded on the leg," a resident said.
Fighting at dawn
At least three civilians were also killed and four wounded by stray bullets and shrapnel from artiliary strikes, residents and local media said.
The fighting broke out at dawn and later settled down, although intermittent blasts of gunfire could be heard across the city.
On Thursday, the UN said about 88,000 Mogadishu residents had fled the city after three days of fighting.
The UN said 46,000 of the displaced people have now taken refuge on the road linking Mogadishu to Afgooye, 30km to the west of the capital.
Another 42,000 have moved to safer neighbourhoods in the capital or areas outside Mogadishu, the UN said.
An unprecidented statement by 39 aid agencies on Thursday said that they were unable to effectivly resppond to the unfolding "humanitarian crisis" in Somalia, caused by insecurity in the country.