Malik had previously remained quiet on the break-up of his relationship with Edwards, 22, who last month called Malik a "bell-end" and hinted that the break-up inspired Little Mix's single Hair.
But he hit back at reports that he ended their engagement by text.
He told the paper: "I love her a lot and I always will, and I would never end our relationship over four years like that.
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"She knows that, I know that, and the public should know as well. I don't want to explain why or what I did, I just want the public to know I didn't do that."
While Malik signed a solo recording contract with RCA Records, One Direction have announced they are to take a hiatus from March next year.
The band said they would be taking a "break" in August and Payne accidentally revealed on BBC Radio 1's Live Lounge last week that it could last two years.
-AAP