The person says Scalise was moved late Thursday, but had no other updates on his condition.
The gunman who shot four people including a Republican member of Congress at a baseball field last week acted alone and was not connected to terrorism, FBI investigators said Wednesday. U.S. Capitol Police and other officers returned fire and killed Hogdkinson, an unemployed home inspector with a deep animus toward President Donald Trump and other Republicans.
Last week, a senior doctor at the hospital said Scalise, 51, had been at the brink of death because of extensive blood loss when he arrived at the hospital by helicopter.
A source familiar with the condition told NBC on Friday that the Louisiana Republican remains in fair condition at MedStar Washington Hospital Center.
The man who carried out the attack, James Hodgkinson, 66, from Belleville, Illinois, was shot dead by police after opening fire, authorities have said.
Scalise's condition was upgraded earlier this week. The VA is the second-largest department in the USA government, with more than 350,000 employees, and it is charged with providing health care and other services to military veterans. He was the most seriously injured victim among the five who were shot last week.
His congressional post as House majority whip, the third-ranking member of the Republican leadership, presumably will remain vacant during the recuperation period.More news: Tim Tebow being promoted to Mets' affiliate in Florida
Hodgkinson had a piece of paper that listed the names of six members of Congress, the FBI investigation revealed.
The FBI also said Hodgkinson had been renting a storage unit in the area since April 16.
James T Hodgkinson did not have any ties to terrorism, said Tim Slater, the special agent in charge of the Washington FBI office.
Hodgkinson's online political rants were mostly anti-Republican and officials said they were within his First Amendment rights. He has required surgery several times since the shooting.
The sheriff said deputies arrived to find Hodgkinson with a hunting rifle on his property where he was apparently engaged in target practice. Bernie Sanders, whose campaign he had worked on as a volunteer, and was in email contact with the two Democratic senators from his home state.
Zach Barth, a legislative correspondent for Rep. Roger Williams, R-Texas, was shot in the leg and released from the hospital the same day of the shooting.
During the assault at the baseball field, Hodgkinson was armed with a 7.62 mm caliber SKS rifle and a 9 mm handgun and fired about 60 rounds, Slater said.