Peyton, a BBC producer, was shot outside her hotel in the Somali capital. Peyton underwent surgery at a local hospital but died later of internal bleeding, according to the BBC.
News reports said Peyton was shot outside the Sahafi Hotel, where she had arrived just hours earlier to begin a series of reports on the strife-torn country. Several foreign reporters were based at the heavily guarded hotel.
Agence France-Presse quoted witnesses as saying that assailants targeted Peyton before speeding off in a white sedan. The vehicle was later found abandoned in a central Mogadishu neighborhood, Mohammed Warsame Doleh, the acting police chief, told AFP.
Peyton's attackers were believed to be two independent militiamen, according to the National Union of Somali Journalists, which conducted its own investigation into the slaying. No official legal action was taken.
The BBC said Peyton had spent the last 10 years in Africa and was based in Johannesburg. She had worked for the BBC since 1993 and had also worked as a producer and trainer for the South African Broadcasting Corporation in Johannesburg.
Foreign reporters had just returned to Mogadishu, where efforts were under way to install a transitional reconciliation government. Local sources said Peyton may have been targeted to discourage foreigners and maintain a climate of insecurity. Violence and lawlessness are rife in Somalia, which has had no effective central government since the fall of dictator Siad Barre in 1991.