A Secret Service spokesperson said in a statement that there was commotion in the crowd at the rally here when an "unidentified individual" shouted "gun," though no weapon was found after a "thorough search".
The man, who later identified himself to reporters as Austyn Crites, was then immediately detained and led out by a throng of police officers, Secret Service agents and SWAT officers armed with assault rifles to a side room.
After he was released from custody, Crites told reporters that the incident started off when he raised a "Republicans Against Trump" sign.
Crites said he was then assaulted by a group of people around him before someone shouted anything about a gun.
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"All of a sudden, because they couldn't grab the sign, or whatever happened, bam, I get tackled by all these people who were just, like, kicking me and grabbing me...And just, just beating me," Crites was quoted as saying by KTNV.
"And somebody yells something about a gun, and so that's when things really got out of hand," he said.
The Secret Service said no weapon was found. "Upon a thorough search of the subject and the surrounding area, no weapon was found," it said.
The 70-year-old business tycoon returned to the stage just minutes after the incident, saying, "Nobody said it was going to be easy for us, but we will never be stopped. We will never be stopped."
"I want to thank the Secret Service. These guys are fantastic," Trump said before returning to his speech.
"I also want to thank the many thousands of people present for their unwavering and unbelievable support. Nothing will stop us -- we will make America great again!" Trump said.
An eyewitness was quoted as saying by NBC News, "I heard, 'He has a gun' and several of us went over to the side wall because we were frightened."
The eyewitness said she was impressed with Trump's composure in continuing the speech.
And a man was arrested at a rally in Las Vegas in June after he tried to grab a police officer's gun, which he said he planned to use to shoot Trump.