The two grabbed each other with Suarez shoving McDowell to the ground.
The two drivers had been jockeying for position on the track just moments before.
Suarez and McDowell downplayed the morning meeting with NASCAR officials prior to practice for the Cup Series race at ISM Raceway, saying they just wanted to ensure no retaliation would take place during Sunday's race.More news: Spurs slump offers chasing Arsenal, Man Utd, Chelsea Champions League hope
"I definitely messed up his lap, but then he tried to crash us. I just didn't appreciate it".
After Suarez got out of his auto having qualified for this race in 28th place, he made his way to the pit box of McDowell, who had not yet emerged from his vehicle following his qualifying run. "You have to qualify well to have a good stall on pit road and obviously to have a good ... race", he said.
"You always have respect for the other drivers, especially here in Phoenix when we all know that the second lap is a good one", Suarez said. "You have to try to get out of the way if someone is coming on their hot lap and he didn't". "I was opening my second lap and he was in my way in Corner 1 and 2".More news: Ayoze Perez sets Newcastle two-win target for survival
"I assumed he was gonna get out of my way in corner three and four and he didn't. And then he was disappointed because I was trying to wreck him afterward". "That's part of racing".
"Heat-of-the-moment stuff", he said. It's racing. Short practice sessions, shorter qualifying, getting late going through tech, the intensity ramps up.
"It was kind of chaotic out there", McDowell said.More news: Passengers evacuated by slides after emergency landing
McDowell qualified 27th, while Suarez qualified 28th.