The gunman opened fire and shot one security guard. Two other security guards returned fire and wounded the suspect, police said.
The suspect was identified as James W. von Brunn, an 88-year-old white supremacist. Sources close to the investigation said that his car was found near the museum and tested for explosives. The weapon was a .22-caliber rifle, they added.
Both the guard and the alleged gunman were taken to George Washington University Hospital in Washington.
A museum spokesperson said the guard, Officer Stephen Johns, died hours later.
"There are no words to express our grief and shock over today's events. Johns served on the Museum's security staff for six years. Our thoughts and prayers go out to Officer Johns's family," said museum spokesperson Sara Bloomfield.
Von Brunn was listed in critical condition.
A third person suffered injuries possibly from broken glass, according to the D.C. fire department. That person was being treated on the scene.
Investigators said James Von Brunn lived in Annapolis, Maryland. His website was listed in 2008 as a hate site by the Southern Poverty Law Center. Von Brunn has a long history of associations with prominent neo-Nazis and Holocaust deniers.
In the 1980s or early 1990s, von Brunn was employed by Noontide Press, a part of the Holocaust denying Institute of Historical Review, which was then run by Willis Carto, one of America's most prominent anti-Semites.
Von Brunn is the author of the 1999 book, "Kill the Best Gentiles," a racist and anti-Semitic tome that argues that whites are seeing "today on the world stage a tragedy of enormous proportions: the calculated destruction of the White Race and the incomparable culture it represents. Europe, former fortress of the West, is now over-run by hordes of non-Whites and mongrels."
In 2003, AP reported that von Brunn had painted a portrait of Rear Adm. John Crommelin, a raging anti-Semite who was a close associate of neo-Nazi William Pierce, whose book The Turner Diaries inspired Timothy McVeigh's bombing of the Oklahoma City federal building.
On his website, von Brunn also claims that in 1981, while wearing a "London Fog raincoat to conceal his weapons," he attempted to put the whole Board of Governors of the Federal Reserve under "legal, non-violent citizens-arrest."
According to police, Von Brunn was arrested in 1981 after an incident in which he pulled a sawed-off shotgun in the Federal Reserve headquarters and warned that he had planted a bomb.
Police at the time said he was distraught over high interest rates and the state of the economy. Guards overpowered Von Brunn before he fired a shot. No bomb was ever found. Writings attributed to von Brunn on the Internet say the Holocaust was a hoax and decry a Jewish conspiracy to "destroy the white gene pool."
"At Auschwitz the 'Holocaust' myth became Reality, and Germany, cultural gem of the West, became a pariah among world nations," it says.
The museum, which opened in 1993 and has drawn nearly 30 million visitors, houses exhibits and records relating to the Holocaust of more than a half century ago in which more than six million Jews died at the hands of Nazis. Its Web site says the museum "teaches millions of people each year about the dangers of unchecked hatred and the need to prevent genocide."
The museum was crowded with school children and other tourists at the time of the attack, but they all escaped injury in the outburst of violence.
The mother of a Massachusetts teenager says students on a school trip to the museum heard several gunshots before they were evacuated from the building.
Sandy Perkins says her daughter, Abigail, called her shortly after the shooting.
Abigail told her mother that some of her friends were very shaken, but all were otherwise fine.
The teens did not see where the shots were coming from before they were safely evacuated to buses outside the museum.
Linda Elston, who is visiting the museum from Nevada City, Calif., said she was on the lower level of the museum watching a film when she and others were told to evacuate.
"It was totally full of people," Elston said. "It took us a while to get out."
She said she didn't hear any shots and didn't immediately know why there was an evacuation. The experience left her feeling "a little anxious," she said.
The museum normally has a heavy security presence with guards positioned both inside and outside the museum. All visitors are required to pass through metal detectors at the entrance, and bags are screened.
The museum, located just off the National Mall near the Washington Monument, is a popular tourist attraction. It draws about 1.7 million visitors each year.
The Museum is closed for the reminder of the day and expects to be open on Thursday.
The White House says President Barack Obama was saddened by a shooting at the Holocaust museum near the White House and is concerned about a guard who was reportedly injured.
White House spokesman Robert Gibbs said he told Obama about the shooting on Wednesday afternoon. Gibbs later told reporters that he gave Obama the facts as they were known at the time, shortly after shots were fired.
Information from ABC News and The Associated Press
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