Officers found an AK-47-style rifle, two rucksacks and a GoPro camera near to where the suspect was spotted on the perimeter of the Trump International Golf Course in West Palm Beach.
US President Joe Biden has said the Secret Service needs more help after Donald Trump was targeted in an apparent assassination attempt on Sunday.
Mr Biden said he was thankful Mr Trump was “OK” before adding he did not yet have a full report of what happened.
He added: “One thing I want to make clear is that the service needs more help and I think Congress should respond to their needs.”
When asked what extra help the service needs, Mr Biden said it might need to be considered whether the service needs “more personnel or not”.
He made the remarks after the FBI said an “apparent assassination attempt” on Mr Trump was thwarted on Sunday, with a man arrested and an assault rifle recovered.
Mr Trump was playing a round at Trump International Golf Course in West Palm Beach in Florida when gunshots were heard.
It is not yet known whether the suspect fired first, fired a round at all or if only the Secret Service fired.
The former US president was on the fifth hole when he was tackled to the ground by security agents fearing an attempt on his life.
The fifth hole in the north-eastern corner of the golf course is just over 300 metres (328 yards) from the southern perimeter fence.
The course is lined with thick foliage, but satellite images show the area between the fence and the approximate point Mr Trump had reached on the course is mostly open water and grass – with the sightline potentially blocked by some trees bordering the lake.
Agent spotted rifle barrel poking out if fence
Palm Beach County Sheriff Ric Bradshaw told reporters that a Secret Service agent, who was patrolling the course ahead of Mr Trump, spotted a rifle barrel coming out of a perimeter fence.
“He immediately engaged that individual, at which time the individual took off,” he said.
Mr Bradshaw said Mr Trump was about 300 to 500 yards (275 to 460m) from the suspect, named as Ryan Wesley Routh, 58, at the time.
Dave Aronberg, Palm Beach County’s state attorney, told MSNBC the suspect was “lying in wait” for Mr Trump.
“We are not sure right now if the individual was able to take a shot at our agents”, Rafael Barros, special agent in charge of the Secret Service’s Miami field office, has told a news conference.
Routh fled in a black Nissan SUV and was arrested after his vehicle was stopped by local police, Sky News’s US partner network NBC News reported, citing three senior law enforcement officials.
He was stopped by police driving northbound on the I-95 highway, about 46 miles and a 43-minute drive from the golf course.
The southern perimeter fence runs along Summit Boulevard, where a police cordon was put up and officers were seen searching the bushes bordering the golf course.
Officers later searched the area where the man, believed to be Routh, was spotted and found an AK-47-style rifle with a scope, two rucksacks and a GoPro.
Earlier, Martin County Sheriff William Snyder described how his officers followed the suspect’s vehicle for a while before making a “felony stop”.
He said: “Our road units picked the vehicle up and we waited a while. We didn’t stop him right away. We didn’t want a high-speed chase.
“So we were able to wait until we had adequate units, surrounded the vehicle, and forced it to a stop.”
He added they managed to take the suspect into custody peacefully.
Routh has since appeared in a federal courtroom in West Bank Palm Beach, Florida.
