[RELATED: Teens inside museum describe scene]
Another law enforcement official said Von Brunn's vehicle was found near the museum and was tested for explosives.
The two officials were not authorized to discuss the investigation and spoke on condition that they remain anonymous.
At a Wednesday afternoon press conference, officials declined to publicly confirm Von Brunn is their suspect.
According to Joseph Persichini, assistant director in charge of the Washington FBI field office, authorities have dispatched people to a suspect's home to check his computer. He said they are investigating this as a possible hate crime or domestic terrorism.
Von Brunn has a racist, anti-Semitic Web site called www.holywesternempire.org and wrote a book called "Kill the Best Gentile."
The U.S. Park Police says the gunman in Wednesday's attack walked into the museum with a "long gun." The gunman and a security guard were shot. A law enforcement source said the gunman was shot in the face, and authorities say he is in critical condition.
In 1983, Von Brunn was convicted of attempting to kidnap members of the Federal Reserve Board. He was arrested two years earlier outside the room where the board was meeting, carrying a revolver, knife and sawed-off shotgun.
At the time, police said Von Brunn wanted to take the members hostage because of high interest rates and the nation's economic difficulties.
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