George Washington University Hospital spokeswoman Susan Griffiths would provide only his condition Saturday, one day after the shooting. She referred other questions to the Secret Service, but a spokesman for that agency, Robert Hoback, declined to discuss the case, citing the continuing investigation.
On Friday, a US law enforcement official said that authorities identified the gunman as Jesse Oliveri of Ashland, Pennsylvania, about 80 miles northwest of Philadelphia.
The official spoke on condition of anonymity because the official was not authorized to release the information.
Iacovetti said the gunman never made it inside the White House complex, and no one else was injured.
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The Metropolitan Police Department, the Secret Service, Park Police and the FBI said in a joint statement Friday night that there was "no known nexus to terrorism."
Messages left Saturday at a home telephone number for Oliveri in Ashland weren't returned.
John Yagielniskie, of Girardville, Pennsylvania, told WNEP-TV that he knew Jesse Oliveri his whole life.
Yagielniskie said Oliveri continued to loyally attend his alma mater's football games after graduating from North Schuylkill High School in 2003.
"Football season starts, I see him. We go to the games. We always go to the games," added Yagielniskie.
Cathy Hadesty, who lives across the street in the wooded area, said police closed a section of the road near the house Friday night but reopened it by Saturday.
Hadesty said she never met Oliveri and only knows the family "just to say, 'Hi,' when we're going down the driveway.