The US President was led out of the news conference and the building was placed on lockdown following the incident.
Mr Trump returned a few minutes later saying the situation was “under control” and the alleged gunman had been taken to hospital.
He told reporters: "There was an actual shooting and somebody's been taken to the hospital.
"It was the suspect who was shot," Trump said.
He confirmed that the shots were fired by police and that he believed the individual who was shot was armed.
The shooting took place just blocks from the White House, according to two sources who were not authorised to speak publicly about it.
Law enforcement officials were still trying to determine the suspect's motive.
The suspect was transferred to a local hospital. Their condition has not yet been confirmed.
Mr Trump praised the work of Secret Service personnel for their work in keeping him safe.
Asked if he was shaken by the incident, the president asked reporters: "I don't know. Do I seem rattled?"