Foreign diplomats urge government to reach out to opposition leaders.
Gun battles between troops and fighters leave dozens dead and wounded.
Somali police said that an operation was under way.
Abduwahid Mohamed, a police spokesman, said: “This operation is aimed at cracking down [on] insurgents who have been killing people in recent months.”
Since Ethiopian and Somali troops defeated the Union of Islamic Courts, a Muslim militia that briefly controlled the capital early this year, Mogadishu has seen a rapid rise in violence, including an increase in crime targeting civilians.
Government forces and AU peacekeepers have failed to quell the violence that has killed hundreds of people and has prevented the delivery of aid to displaced civilians in and around the capital.