Gedi said the clan leaders would now work with his administration to take on the fighters.
Ahmed Diriye, a Hawiye spokesman, told Reuters that the interim government and fighters both had a responsibility to end the violence.
"If the truce gets enforced, I do hope that all people who have political agendas on their mind, opposing the government, will compromise with it," he said.
Responding to accusations that government troops have been heavy-handed in their hunt for fighters, Gedi called on army officers to control their men.
Gedi's government - the 14th attempt to introduce central rule in Somalia - has struggled to impose its authority in the face of roadside bombings, grenade attacks and assassinations.
But Mogadishu has been relatively calm in recent days, and the outcome of Gedi's meeting with the clan leaders was eagerly anticipated by many war-weary residents.