Ali Sheik Yasin Fadhaa, the vice-chairman of the local Elman Human Rights Organisation, said: "Some of them do not know where to go. They need urgent help."
Fadhaa said that his staff throughout Mogadishu had counted at least 5,200 people fleeing on Monday, taking the total since Saturday to more than 17,000.
While vowing to defend his government, Sharif Ahmed has endorsed plans to introduce Islamic law, a key demand by the fighters for their co-operation with his administration.
However, several armed groups such as al-Shabab and Hizbul Islam have refused to hold talks with him, saying Sharif Ahmed is too close to the West.
Years of conflict in Somala has killed tens of thousands, displaced millions and created a security vacuum that has spawned piracy in the Gulf of Aden.