Abdirahman Dinari, a spokesman for the Somali government said the troops "will not stop the chase until we are sure they are totally eliminated."
"Most of the wanted terrorists have either died or fled," he said.
The US sent a military aeroplane into Somalia on Monday to try to kill top al Qaeda suspects and Ethiopian aircraft have bombed the area for days.
"Peace is possible if the interests of US and the Ethiopians are removed"
Ahmed, Bossaso, Somalia
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The aid agency Oxfam said air raids to pursue fleeing fighters and their suspected al Qaeda allies hiding in southern Somalia had mistakenly killed 70 nomadic herdsmen.
While some Somali sources have reported scores of deaths, there has been no independent confirmation. Both Ethiopia and the United States deny hitting civilians.
Washington says its strike killed up to 10 al Qaeda allies, but missed its main target of three top suspects and denies carrying out any further strikes.
Elsewhere witnesses said Ethiopian troops scouring southern Mogadishu for weapons were particularly interested in heavy artillery that might be used against aircraft arriving in the city which continues to operate outside the rule of law.
"The Ethiopian troops are searching house-to-house and they were looking for weapons and Islamist fighters," Abdi Ibrahim, a shop owner in the Bullohabey neighbourhood, said.
But residents in the neighbourhood, where the joint Ethiopian-Somali troops are located, said many had buried their weapons.
"Most people buried their weapons and it is very difficult for them to get the arms. Also, heavy weapons have been dismantled and kept separately in small pieces," Daud Hassan, another Bullohabey resident, said.