Sheikh Ahmed said the meeting was "to establish a political organisation that liberates the country and ends the violence and chaotic situation".
"We call upon Ethiopia to unconditionally withdraw its troops from Somalia and stop its imperialistic adventure on our territory," he said.
He warned that a prolonged conflict in Somalia would eventually spill over into neighbouring countries.
"We remind her [Ethiopia] that the longer the conflict goes on, the higher the risk it will engulf the whole region," he said.
"The United States' foreign policy towards Somalia has been strangely confrontational. We call upon the United States to play a more positive role in the Somali conflict."
Wanted by the US
Sheikh Aweys and other members of the Islamic Courts Union are wanted by the US over suspected links to al-Qaeda.
The US has backed Ethiopia's military operations in Somalia and toughened its stance towards Eritrea, Ethiopia's neighbour and long-time enemy, which Ethiopia says has been arming groups in Somalia and elsewhere in the region.
The Islamic Courts had boycotted the earlier clan reconciliation conference in Mogadishu, arguing that any peace efforts should take place only after an Ethiopian withdrawal.
In its three years of existence, Somalia's Western-backed transitional government has failed to restore stability, spending much of that time controlling only a small portion of the country.
It blames the Islamic Courts and its allies for the near-daily attacks which have plagued Mogadishu in recent months.
Three people were killed on Thursday in the latest spate of fighting between government forces and armed groups in Mogadishu.
Ali Mohammed Anwar, a witness to the incident, told the AFP news agency that an elderly man and a woman were killed when a police patrol came under grenade attack near the capital's Salama mosque.