Republican presidential candidate Donald Trump is safe after what the FBI says appeared to be an assassination attempt while he was golfing on his course in West Palm Beach, Florida.

Law enforcement officials said US Secret Service agents spotted and fired on a gunman on Sunday in some bushes near the property line with an AK-47-style assault rifle.

The New York Times and Fox News Channel identified the suspect as Ryan Wesley Routh, 58, of Hawaii, citing unnamed law-enforcement officials.

After spotting the rifle barrel about 350-450m away from Trump as they cleared holes of potential threats ahead of his play, the agents engaged the gunman and fired at least four rounds of ammunition, Palm Beach County Sheriff Ric Bradshaw told a news conference.

The gunman then dropped his rifle, two backpacks and other items and fled in a black Nissan car. A witness, the sheriff said, saw the gunman and managed to take photos of his car and licence plate.

Pictures of evidence found at the fence of US president Donald Trump's golf course are shown at a press conference in West Palm Beach, Florida. Photo / AFP

“The Secret Service did exactly what should have been done,” Bradshaw said.

After Routh fled the scene, law enforcement officials sent out an alert to statewide agencies with the information on his vehicle, which led to sheriff’s deputies in neighbouring Martin County apprehending the suspect on I-95.

“We have somebody in custody right now,” said Bradshaw, who did not identify the suspect or give details on a possible motive.

Trump sent an email to his fundraising list saying there were “gunshots in my vicinity, but before rumours start spiralling out of control, I wanted you to hear this first: I AM SAFE AND WELL!” according to an email seen by Reuters.

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Trump was injured in an assassination attempt in Pennsylvania on July 13, raising questions about protection for candidates just months ahead of what looks likely to be highly contested November 5 election in which he will face off against Democratic Vice President Kamala Harris.

The White House said in a statement that President Joe Biden and Vice President Kamala Harris had been briefed about the incident and were relieved to know that he is safe.

“Violence has no place in America,” Harris said on X.

Trump’s running mate in the presidential election, US Senator JD Vance, said he spoke to Trump after the shooting and that the former president was in good spirits. The first shooting of a US president or major party presidential candidate in more than four decades was a glaring security lapse that forced Kimberly Cheatle to resign as Secret Service director under bipartisan congressional pressure.

Trump was grazed in the right ear and one rallygoer was killed in the gunfire. The gunman, identified as a 20-year-old Thomas Crooks, was shot and killed by a Secret Service sniper.

The Secret Service’s new acting director said in August that he was “ashamed” of a security lapse that led to the assassination attempt.