The shooting suspect was identified as Cole Tomas Allen, 31, of Torrance, California, two law enforcement officials told The Associated Press.
Addressing reporters at the White House after he and other top US leaders were evacuated from the dinner, Trump said the suspect was in custody. One officer was shot, but he was protected by a bulletproof vest.
"He was shot from very close distance with a very powerful gun, and the vest did the job," Trump said.
As he began the news conference, Trump called for tougher security measures, saying that "today, we need levels of security that probably nobody has ever seen before".
Security footage posted by Trump shows a man sprinting through the metal detectors and past law enforcement, who turn toward him with guns raised. Officers then swarm toward the man off-screen.
The secret service and other authorities rushed into the banquet hall at the Washington Hilton as guests ducked under tables by the hundreds.
Audible gasps echoed through the ballroom as guests realised something was happening. Hundreds of journalists got on phones to call in information.
"Out of the way, sir!" someone yelled. Others shouted to duck. From one corner, a "God Bless America" chant began as the president was escorted offstage.
He fell briefly - he apparently tripped - and was helped up by Secret Service agents. Outside the hotel, members of the National Guard and other authorities flooded the area as helicopters circled overhead.
Authorities said the incident occurred outside the subterranean ballroom where Trump and other guests were seated. After an initial attempt to resume, the event was scrapped for the night and will be rescheduled.
"We will do this again," said Weijia Jiang, president of the White House Correspondents' Association.
All officials protected by the Secret Service were evacuated. Those in attendance included Trump, Vice President JD Vance, Defence Secretary Pete Hegseth and Secretary of State Marco Rubio — and many other leaders of the Trump administration.
House Speaker Mike Johnson said he and his wife, Kelly, who both attended the event, were "praying for our country tonight".
The House Democratic leader, Hakeem Jeffries of New York, said, "The violence and chaos in America must end."
Some in the crowd reported hearing what they believed to be five to eight shots fired.
The banquet hall - where hundreds of prominent journalists, celebrities and national leaders were awaiting Trump's remarks - was immediately evacuated.
Members of the National Guard took up position inside the building as people were allowed to leave but not immediately reenter. Security outside was also extremely tight.
Republican Mike Lawler of New York, a guest at the dinner, said he heard a pop and "we didn't know what the hell it was. And then you heard all sorts of things clatter."
Lawler said he gets "death threats often" and said, "I think we live in a climate where everybody recognises its a problem, but I don't think people fully appreciate how much of a problem it really is."
