The suspect was transferred to a local hospital, and the District of Columbia fire department said the man suffered serious or possibly critical injuries.
The president said the situation "seems to be very well under control". "And the suspect is on the way to the hospital", he said.
"I do want to thank the Secret Service".
Asked if he felt rattled by the security scare, Mr Trump responded: "Do I seem rattled?"
Trump went on to praise the US Secret Service, which is in charge of guarding the president, as "fantastic people, the best of the best".
The Washington Post's Jennifer Rubin was shredded online for quipping that it was time for a "bunker inspection" after the Secret Service rushed the president out of a press briefing, seemingly elated that he might be in danger.
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Treasury Secretary Steve Mnuchin and Office of Management and Budget Director Russ Vought were also taken out of the room and the doors were locked.
President Donald Trump's lawyers made a final pitch Monday to block a NY prosecutor from getting his tax records, saying the Democrat was still "fishing for a way to justify his harassment of the President". "He was outside and he heard two shots", he added.
The incident happened on the corner of 17th Street and Pennsylvania Ave, which is outside the perimeter of the White House.
Trump said he was escorted to the Oval Office by the agent.
"It's unfortunate that this is a world but the world has always been a unsafe place; it's not something that is unique".
"I feel very safe with the Secret Service", Trump said. 'I asked if I was able to come back, they said to wait a little while'.