President Trump is giving a press conference Saturday night at the White House shortly after being evacuated from the nearby White House Correspondents' Dinner after shots were fired at the hotel where the event was taking place.

The president said one Secret Service agent was struck by a round but was protected by a bulletproof vest. Mr. Trump said he was "very far away" when the shots rang out and said the suspect "hadn't come anywhere close to breach the doors of the room." 

Mr. Trump said he had ordered for "the tape showing the violence of this thug that attacked the Constitution, and also showing how quickly Secret Service and law enforcement acted." 

The evacuation occurred just after 8:30 p.m. ET after the sound of gunfire sent attendees scurrying and ducking under tables. Mr. Trump and first lady Melania Trump were whisked off the stage by Secret Service agents. Three sources told CBS News that the suspect has been identified as 30-year-old Cole Allen of Torrance California.

The suspect is in custody and hospitalized, officials said. The suspect had a shotgun and handgun on him, according to two sources familiar with the investigation into the shooting. Acting Attorney General Todd Blanche said the investigation is "ongoing," and charges will be filed "shortly. 

Mr. Trump said he "heard a noise" and thought it was a "tray going down." 

"But it was a gun," the president said. "And some people really understood that pretty quickly, other people didn't. I was watching to see what was happening, probably should have gone down even faster. Melania was very cognisant, I think, of what happened. I think she knew immediately what happened." 

"We were whisked away, along with other people, but we were really whisked away," he added. 

One officer was shot, but "saved by the fact that he was wearing a, obviously, a very good bulletproof vest, he was shot from very close distance with a very powerful gun," the president said. "The vest did the job."

The president said he spoke with the officer, and described him as being in good spirits.

"This was an event dedicated to freedom of speech that was supposed to bring together members of both parties with members of the press," the president said. "And in a certain way it did. Because the fact that they just unified, I saw a room that was just totally unified. It was, in one way, very beautiful, a very beautiful thing to see." 

Mr. Trump said the event would be rescheduled within the next 30 days. He added that he "fought like hell" to keep the event going, but law enforcement insisted otherwise. 

White House Correspondents Association President and CBS News correspondent Weijia Jiang asked Mr. Trump what he was feeling when it occurred, particularly after he was shot in Butler, Pennsylvania. Mr. Trump said "it's always shocking when something like this happens. Happened to me, a little bit. And that never changes."