Donald J. Trump announced from the stage at a rally in Kansas City, Mo., that a man who had charged him at an event earlier Saturday was “probably” linked to the Islamic State, appearing to base his statement on an Internet video that has been described as a hoax.

“This was a guy that was looking to do harm,” Mr. Trump said at his last event of the day. “It was probably ISIS or ISIS-related, can you believe it?”

He added that “my people found this” on the Internet, and just before the rally he posted it on Twitter.

USSS did an excellent job stopping the maniac running to the stage. He has ties to ISIS. Should be in jail! https://t.co/tkzbHg7wyD?ssr=true — Donald J. Trump (@realDonaldTrump) March 12, 2016

Earlier Saturday, in Dayton, Ohio, a man jumped a barrier and rushed toward the stage, causing a brief scare as Secret Service agents surrounded Mr. Trump. The man was tackled and taken away.

Later, a video surfaced purporting to show the same man at a protest months ago. That video was taken and overlaid with Arabic text and music, but it appears to have been done as a hoax. No government agency has suggested that the man was connected to terrorism.

But that did not stop Mr. Trump from insisting that there was a more sinister threat.

“Certainly he’s not in love with our country, that I can tell you,” he said.

Mr. Trump said that in the future he would press charges against protesters to deter them because “their lives are going to be ruined, and they’ll know their lives are going to be ruined.”

Demonstrating his point later, when a woman shouted during the rally, he called out, “Arrest her. Arrest her.” (It was unclear if she was arrested.)