"It was horrible. I heard the plane flying very low, then I heard the explosion," Camille Avfert, a witness, said. "We ran out onto the street and saw fire."
One of the dead on the ground was identified as Elena Reascos, the mother of a nine-year-old boy.
"I was with my mother in the house when I heard something crash and there was an explosion," he said.
"The flames were everywhere. I couldn't get out of my room, and the firefighters rescued me."
The aeroplane was on a training run at the time of the accident, Javier Ponce, Ecuador's defence minister, said.
Fog often causes aviation difficulties and delays in Quito and witnesses said the weather was bad when the crash happened on Thursday.
In September last year, a passenger jet carrying more than 60 people skidded off a runway and crashed through a brick perimeter wall before stopping near a busy road in Quito, but no one was seriously hurt.