Sudan Ali Ahmed said his group was accused of spreading "exaggerated and false information" about the country's fragile government.
Mogadishu Mayor Mohamed Dheere ordered Elman Human Rights, an independent Somali group, to close its offices on Oct. 8, Ahmed said, adding he had waited more than a month to go public as he tried and failed to reach senior government officials.
The Associated Press obtained a copy of a letter from Dheere in which he orders Elman officials "to stop your ongoing business ... for security reasons."
Dheere could not immediately be reached for comment as his cell phone want unanswered. Others government officials were also not immediately available for comment.
"I'm a wanted person," Ahmed said by phone from an undisclosed location in Mogadishu. "Government soldiers are searching for me everywhere. I stay in different places in the capital. The world should stand up and intervene to save Somali people from their own government that abuses the basic rights of its citizens."
Elman Human Rights has 116 staffers who work across the country. The group has tracked the killings of civilians during Mogadishu's near daily violence this year and has also reported on violations in recent years.
Several human rights groups have accused the government, insurgents and Ethiopian troops of committing abuses.
Ethiopia came to the aid of Somalia's fragile government in December to rout an Islamic group called the Council of Islamic Courts. The Islamic group's fighters then threatened an Iraq-style insurgency, and thousands of Mogadishu residents have been killed this year in the capital's near daily round of gunbattles, grenade and mortar attacks.
In a separate development, the four local radio stations left broadcasting in Mogadishu said on Monday that they would go off the air for 24 hours in solidarity with other radio stations closed by the government, to "pressure the government to allow them back on air," they said in a statement. The broadcasters are Voice of the Democracy, Voice of the Quran, Somaliweyn and HornAfrik.
Last week, the government shut three private radio stations for allegedly airing inflammatory broadcasts and ordered all media houses in the country to seek registration or face closure.
Somalia has not had a functioning government since a group of warlords overthrew dictator Mohamed Siad Barre in 1991, then turned their heavily armed supporters on each other.