"We need the wall, and it has to be built, and we want to build it fast," he said, as people chanted, "Build that wall!" "Now, you really mean finish the wall," Trump responded.
Skeans, the cameraman, told BBC News that he did not see the Trump supporter coming at him but felt a "very hard shove" that almost knocked him down.
"I didn't know what was going on," he said.
Video from Skeans' camera showed it fall toward the ground. Seconds later, when the picture was restored, a man in a red "Make America Great Again" hat could be seen being restrained as he shouted, "[expletive] the media!"
BBC Washington correspondent Gary O'Donoghue said on Twitter that a rally attendee had jumped onto the media platform, "tried to smash our camera" and shoved his colleague, Skeans.
A photographer based in El Paso also tweeted a video from another angle, writing, "just had a man shove photogs and equipment over."
A reporter for the Washington Examiner wrote on Twitter that leading up to the altercation, Trump had "railed against all the media." But after the incident, Trump pointed toward the crowd and asked, "You all right? Everything OK?"
The president then flashed a thumbs up.