The five minute video shows footage of Tomlinson and Malik sharing a joint while travelling in Peru.
Tomlinson narrates as a joint is passed between the boys, saying: "So, here we are, leaving Peru. Joint lit. Happy days."
He then turns the camera toward the smoking Malik and says: "That's just Zayn warming up before the show."
Adding: "One very, very important factor to Zayn's warm-up, of course, is Mary J herself."
The footage is thought to have been stolen from the band, before it was leaked to the Daily Mail.
The comments from Payne were provoked by an article written by Daily Mail writer Jan Moir.
In the article, Moir questions the bands musicianship and claims the One Direction boys "like so many before them, take fame for granted."
In response, Payne wrote: "I think you'll find I've written a lot of the next album and songs on the last I play piano and Niall plays guitar that ok?"
Think you'll find I've written a lot of the next album and songs on the last I play piano Niall plays guitar that ok? pic.twitter.com/GLOa0H3LaT
He then mimics Moir by writing: "like so many writers before, consistently get things wrong looking down there (sic) noses thinking they are so right."
He ends the lengthy apology by saying: "Hopefully we stand the test of time and get it right in the end," adding "I don't take this for granted and im (sic) extremely grateful to be here doing this."
- Independent