The crew of the twin-engine aircraft belonging to Noar Airlines reported problems shortly after taking off about 7 a.m. (6 a.m. EDT; 1000 GMT) from the city of Recife en route to the city of Natal.
The Air Force did not indicate what the problems were or what caused the crash, but said it is investigating.
The pilot tried to make an emergency landing in a vacant lot near a beach on the outskirts of the city's center, near several apartment buildings. But witnesses said the aircraft went down hard and burst into flames.
Noar Airlines' website says it began operations in June 2010 and that it makes 278 flights a week. It owns a fleet of four small planes.