Daramola told Xinhua the crash occurred as the two jets were rehearsing for Nigeria's 58th independence anniversary celebrations.
The pilot flying an F7-Ni jet was killed on the spot.
Mohammed Gidi Nass, who led a rescue team before the arrival of emergency officials and military personnel, told Xinhua they carried one dead body and rescued three others.
Among the three rescued, one was injured and two were unhurt.
A witness living nearby said earlier a big bang was heard before he saw heavy smoke arising from a mountain behind his office in the Katampe area of Abuja, and two pilots were spotted landing with parachutes.
Nigerian defense ministry spokesman John Agim confirmed the accident to Xinhua via telephone.
"Our men are still at the crash site, working. We shall address the media after the ongoing emergency operation," he said.
Nigeria will hold a grand ceremony on Monday celebrating the 58th anniversary of the country's independence.