Mohamed, a resident close to the scene of the clashes, said: "Anybody who has any means of fleeing the area has left."
After a night of sporadic fire, heavy explosions hit Mogadishu's northern districts on Monday, residents said.
Mukhtar Mohamed, a resident of Fagah in northern Mogadishu, said: "I have seen Ethiopian tanks taking positions and heavily shelling insurgent positions.
"The fighting is heavier [than] yesterday, the rivals are exchanging machine guns, mortar and anti-aircraft fire."
Several civilians have been trapped in the area as scores of rotting corpses lay abandoned on the streets, where Ethiopian tanks and modified pick-up trucks raced with fighters aboard firing recklessly.
Hussein Said Korgab, the spokesman for the Hawiye clan, Mogadishu's largest, said: "The fighting is very heavy and the casualties are steadily increasing everyday. The Ethiopian forces are hitting civilians indiscriminately."
The clashes, which erupted on Wednesday, have so far killed 219 civilians and wounded hundreds others, according to the Elman Peace and Human Rights Organisation which tracks casualty figures.
This week's flare-up alone has displaced at least tens of thousands and destroyed property of massive value, Korgab said.
He said: "At least 70,000 have evacuated their homes. Property worth $500m has been destroyed. The Ethiopian and government forces will take ultimate responsibility for all these mess."
Four days of fighting earlier this month claimed at least 1,000 lives in clashes that were described as the worst bloodletting since 1991, when Mohamed Siad Barre, Somalia's then-military ruler, was ousted from power.
The United Nations says about 321,000 people have fled Mogadishu since February. Many are camped under trees and makeshift hovels in the city's outskirts, without supplies and where disease outbreaks have been reported.