Mr Trump acknowledged it was an unusual situation, but praised the professionalism of the USSS.
A journalist asked Mr Trump if he was rattled by the events.
"Do I seem rattled?" he replied.
The president added: "It's unfortunate that this is the world, but the world's always been a dangerous place. It's not something that's unique.
"The world has been, if you look back over the centuries, the world has been a dangerous place, very dangerous place, and it will continue, I guess, for a period of time."
He told journalists he was escorted to the Oval Office outside the briefing room during the incident.
Also led out of the news conference were Treasury Secretary Steve Mnuchin and Office of Management and Budget Director Russ Vought. The doors were locked.
The District of Columbia fire department said a man suffered serious or possibly critical injuries, according to the Associated Press.
The news agency also reported that authorities were looking into whether the individual has a background of mental illness.