Nigerian authorities say the death toll from a plane crash outside Lagos international airport's domestic terminal has risen to 16.

The small passenger aircraft, operated by Nigeria's Associated Airlines, carrying 20 people crashed in Nigeria’s commercial capital shortly after take-off on Thursday.

Sixteen people were killed and four others survived, said Usman Muktar, commissioner of the Accident Investigation and Prevention Bureau.

According to local media reports, the plane was carrying the dead body of a former regional governor, and several members of his family.

"The plane was making a lot of noise before it came down," said Rasheed Olajide, an engineer at the airport.

"I heard a loud bang and then there was lots of black smoke. The security forces rushed straight to the scene. I saw three bodies removed from the wreckage," eyewitness Ahmad Safian said.

The plane was flying to Akure, a town east of Lagos when it went down.

Nigeria has had a list of deadly plane crashes. At least 159 people died in June, when a flight from domestic company Dana Air crashed in Lagos after both its engines stopped working.