The NAF suggested the accident was due to a plane crash.
The video was published by SITE Intelligence Group and is circulating in the Nigerian media.
“It is clear that most parts of the video were deliberately publicized to give the false impression that the aircraft was shot down” when it was “obviously a plane crash,” NAF said in a statement posted on Facebook on Friday.
The NAF rejected the seven-and-a-half-minute edited video, calling it “false propaganda” and urging Nigerians “to ignore the content of the videos that make the round until all investigations into how the plane crashed are completed.”
NAF reported the disappearance of the plane on Wednesday, with two pilots on board.
A spokesman told CNN on Thursday afternoon that the fighter jets were deployed near Borno State in northeastern Nigeria to provide air support to ground troops under fire from Boko Haram fighters before radar contact was lost.
“The cause of the accident, as well as the location of the two pilots, remain unknown. The pilots are flight lieutenant John Abolarinwa and flight lieutenant Ebiakpo Chapele,” NAF said earlier on Friday.
In the disputed video, Boko Haram claims to have shot down Alpha Jet.
The footage shows several fighters firing into the air before an explosion ignites the sky while a plane ignites in flames and falls to the ground. The video then addresses the fighters standing around what appears to be the wreck of the jet.
Then it goes to the plane, displaying “NAF 475” – the missing aircraft identification number. Later it shows a charred body.
Separately, the video then shows what appears to be a patch placed on the ground, displaying the name of John Abolarinwa.
CNN cannot independently verify the authenticity of the video.
Boko Haram has stepped up attacks on the Nigerian military as it seeks to regain control of lost territory in the pockets of the country’s northeast.
Frequent airstrikes by the Nigerian army continued to shake insurgents – driving them out of their hiding places.