The shooting happened near 17th St and Pennsylvania Ave just blocks from the White House, according to two sources with knowledge of the situation but who were not authorised to speak publicly about it.
Law enforcement officials were still trying to determine the suspect's motive.
Trump says he's 'very safe'
"Was the suspect armed?" one of the reporters asked on his return.
"From what I understand, the answer is yes," Trump replied. "That's what I understand. I don't know. You'll have to ask them."
Asked whether the suspect had said anything about him, Trump said he didn't know.
"It might not have had anything to do with me. It might have been something else," he said.
"But it was on the outside of the premises. The wall - as you know, the fencing, especially the new fencing that they put up, is very powerful. But it was on the outside of the White House.
"It's unfortunate that this is a world - but the world's always been a dangerous place. It's not something that's unique. The world has been - you look back over the centuries, the world has been a dangerous place.
"It will continue, I guess, for a period of time."
Trump stressed that he feels "very safe with the Secret Service".