WASHINGTON — The Air Force has been secretly flying armed Reaper drones on counterterrorism missions from a remote civilian airport in southern Ethiopia as part of a rapidly expanding U.S.-led proxy war against an al-Qaida affiliate in East Africa, U.S. military officials said.

The Air Force has invested millions of dollars to upgrade an airfield in Arba Minch, Ethiopia, where it has built a small annex to house a fleet of drones that can be equipped with Hellfire missiles and satellite-guided bombs. The Reapers began flying missions earlier this year over neighboring Somalia, where the United States and its allies in the region have been targeting al-Shabab, a militant Islamist group connected to al-Qaida.

Mindful of the 1993 “Black Hawk Down” debacle in which two U.S. military helicopters were shot down in the Somali capital of Mogadishu and 18 Americans killed, the Obama administration has sought to avoid deploying troops to the country.