He added the arrangements were likely to change going forward.
The golf course was partially shut down for Trump as he played, and agents were a few holes ahead of him when they noticed the gunman, officials said.
Secret Service agents and officers in golf carts and on ATVs generally secure the area several holes ahead and behind Trump when he golfs.
Joe Biden and Kamala Harris were briefed on the suspected assassination attempt, the White House said.
“They are relieved to know that he is safe. They will be kept regularly updated by their team,” an official said.
The 78-year-old Republican candidate was later escorted back to his main residence, Mar-a-Lago, about five miles away on Palm Beach.
In a fundraising appeal following the incident, Trump reiterated that he was “safe and well”.
“Nothing will slow me down. I will NEVER SURRENDER!” he said.
JD Vance, Trump’s running mate, said Trump was “amazingly, in good spirits” following the incident.
“I’m glad President Trump is safe,” Mr Vance said. “Still much we don’t know, but I’ll be hugging my kids extra tight tonight and saying a prayer of gratitude.”