Donald Trump has praised an “amazing” woman motorist who he said tailed an alleged gunman as he made his getaway after an apparent assassination attempt on the former president on Sunday, leading to a speedy arrest.

In his first public appearance since the incident, the Republican presidential candidate told a crowd that the unnamed civilian “saw something in this guy that was bad”.

She spotted the suspect running to his car and became suspicious, so followed him in her own vehicle and took pictures of his licence plate, Trump said.

Ryan Wesley Routh, 58, was arrested in an SUV less than an hour after he allegedly fled Trump International Golf Club in West Palm Beach, Florida.

Trump shared the account on Tuesday night at a town hall-style event in Flint, Michigan, with Sarah Huckabee Sanders, his former press secretary and now governor of Arkansas.

Trump was rushed to safety unharmed after Secret Service agents spotted a muzzle of a rifle sticking through the shrubbery as the former president was playing a round of golf.

The Republican candidate was about 300-500 yards (275-460m) away.

An agent shot in the direction of the apparent sniper’s nest before the suspect dropped the rifle and fled into a black Nissan SUV, police said.

“You want to know another sort of a miracle?” Trump told the crowd after lauding the Secret Service. “So the guy's now running for his life, and he's got a car a block away or whatever.”

He added: “And a woman, driving in a car, saw a man on the street, pretty busy street, running.

“And she followed him. And he got into the car. And she stopped because she thought he was trouble. He looked different.

“She followed him, it wasn't very far, and parked the car behind his car and started taking pictures of his licence plate.”

“Seriously, who would do that?” he said, adding that “she was really amazing”.

Trump said she quickly sent those images to the authorities.

“Women are smarter than men,” he told the crowd, adding that he would like to meet her.

Routh was stopped by police driving northbound on the I-95 highway.

He appeared in court on Monday, charged with possession of a firearm by a convicted felon and possession of a firearm with an obstructed serial number. More counts could follow.

It was apparently the second assassination attempt targeting Trump in as many months.