The man was identified as Myron Berryman, 51, and is expected to face federal assault charges, the officials said. He remains in hospital with critical injuries.
The officials, who were briefed on the investigation, could not discuss the ongoing probe publicly and spoke to The Associated Press on condition of anonymity.
Berryman had approached the uniformed officer just before 6pm on Monday at the corner of 17th Street and Pennsylvania Avenue, just blocks from the White House, and told the officer he had a weapon, secret service uniformed division chief Tom Sullivan said.
He then moved aggressively toward the officer and appeared ready to fire before the officer shot him once, Mr Sullivan said.
Before the shooting, Berryman had been shouting that he was going to kill people, according to the officials familiar with the matter.
Mr Sullivan would not answer questions on Monday night about whether the man had indeed been armed, but no weapon was recovered at the scene, the officials said.
The White House complex was not breached and no one under secret service protection was in danger, Mr Sullivan said.
Law enforcement officials were still trying to determine a motive and authorities were investigating whether the man had a history of mental illness.
President Trump had just begun a coronavirus briefing when a US secret service agent escorted him from the briefing room.
The president returned minutes later, saying there had been a “shooting” outside the White House that was “under control”.
“There was an actual shooting and somebody’s been taken to the hospital,” President Trump said.
The president said law enforcement had fired the shots and that he believed the individual who was shot was armed. “It was the suspect who was shot,” he said.
President Trump said the agent had escorted him to the Oval Office. The White House was placed on lockdown following the incident.
At the White House, President Trump praised Secret Service personnel for their work in keeping him safe. Asked if he was shaken by the incident, he asked reporters: “I don’t know. Do I seem rattled?”
