Masvidal, while doing a live interview with ESPN, left midway through to confront Edwards. Masvidal then threw a few punches toward Edwards' face, leaving a cut beneath his left eye.
On Monday, Edwards spoke about the incident for the first time.
"We were both doing media," Edwards said on Ariel Helwani's MMA Show. "I was walking past. He was staring at me. I said, 'Are we fighting in July?' He walked out of his interview. I walked towards him, as well. And then he threw two shots, and that was it.
"It's a bunch of nonsense really. But his day will come."
Masvidal told ESPN's Brett Okamoto late Saturday night that he was "defending myself" because "this hooligan threatened my life."
"I had my hands back to signal I'm not coming here with problems," Masvidal said. "But he put his hands up, it's on video, and walks towards me. Well, where I'm from, you do that, you're going to punch me in the face. And that's not going to happen.
"I gave him a three-piece with the soda and just glide out of there."
Edwards, who said he received two stitches for the cut, said Masvidal's reasoning was a bunch of lies.
"Who does that? Why would I walk towards him with my hands up?" Edwards said. "If I did do that, he wouldn't be able to land nothing on me. He threw a few shots, and the security grabbed us back, and that was it. That was the whole situation. He got away this time, but it will never happen again."
The backstage altercation overshadowed stellar performances for both Masvidal and Edwards.
Masvidal (33-13) bounced back from a two-fight skid to knock out former UFC welterweight title challenger Darren Till in the second round in his opponent's home country.
Edwards (17-3) is now on a seven-fight win streak after soundly defeating Gunnar Nelson in three rounds.
"What I did Saturday to Gunnar Nelson -- that should be the main topic," Edwards told Helwani on Monday. "I feel I deserve the title shot right now. But that fight [against Masvidal] has to happen either before or after. That fight will happen."