The man approached a checkpoint shortly after 6pm on Saturday, "removed a weapon from his bag and began firing at posted officers", the US Secret Service said in a statement.
Officers returned fire, hitting the gunman, who was transported to hospital, where he later died.
The man was identified as an emotionally disturbed person, a law enforcement official told Reuters, adding that a "stay-away order" had been issued to him previously.
A bystander was also struck, but a law enforcement official said it wasn't clear whether that person was hit by the suspect's bullets or those fired subsequently by officers.
The Secret Service said none of its officers were injured, and that President Donald Trump - who was at the White House at the time - was not "impacted".
Journalists working at the White House on Saturday evening reported hearing a series of gunshots and were told to seek shelter inside the press briefing room.
The Secret Service said on X it was "aware of reports of shots fired near 17th Street and Pennsylvania Avenue NW" - one block from the White House - and was "working to corroborate the information with personnel on the ground".
In a social media post, FBI Director Kash Patel said officers were responding to shots fired and said he would "update the public as we're able".
In a post shared on X, Selina Wang, the senior White House correspondent for ABC News, shared dramatic video of the moment she said she heard what "sounded like dozens of gunshots" and ducked for cover.
Writing that she had been performing a task that reporters at the White House do day in and day out - filming themselves on a mobile phone, for a social media post - Wang's video shows her speaking for a few seconds about Trump's statements earlier on Saturday about a potential Iran deal.
As the sounds of gunfire are heard in the background, Wang's eyes grow wider, and she ducks down in the media tent, which is among those situated in a line along the White House driveway where broadcasters film their reports.
Wang's video had been shared thousands of times and viewed at least three million times.
The Metropolitan Police Department said on X the Secret Service was working the scene and cautioned people to avoid.
The scene is near where a gunman ambushed two members of the West Virginia National Guard last November.
US Army Specialist Sarah Beckstrom, 20, died from her wounds. Andrew Wolfe, then 24, was critically wounded. Rahmanullah Lakanwal has been charged in that incident.
The gunfire on Saturday comes nearly a month after what law enforcement authorities said was an attempted assassination of the president on April 25 as he attended the annual White House Correspondents' Association Dinner at a Washington hotel.
Cole Tomas Allen, of Torrance, California, recently pleaded not guilty to charges that he attempted to kill Trump and remains in federal custody.
Following that scare, Secret Service officers shot a suspect they said had fired at officers near the Washington Monument, also near the White House.
Michael Marx, 45, of Midland, Texas, was charged in a complaint filed in US District Court in connection with the May 4 shooting. A teenage bystander was wounded in that incident.
with AP
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