Scalise, 51, who represents a district in Louisiana and is the House majority whip, had previously been listed in critical condition. "The Scalise family greatly appreciates the outpouring of thoughts and prayers", the hospital wrote, "on behalf of the Scalise family".
It includes photos of Scalise and his family.
Medical staff also have removed a tube that had been inserted into Scalise's abdomen to prevent fluid from going into his lungs while he was sedated, said the sources, who spoke on the condition of anonymity because they were not authorized to comment on the congressman's medical status.
On Friday, the hospital's director of trauma, Dr. Jack Sava, called Scalise's injury a "transpelvic gunshot wound" which had "fragmented, and caused significant damage to bones, internal organs and blood vessels".
The person did not disclose the names, but said those listed had been briefed. "He underwent another surgery today, but continues to show signs of improvement".
The shooter, James T. Hodgkinson, was killed by police Wednesday after firing dozens of bullets during the congressional practice session.
Since then, the lawmaker has undergone multiple surgeries and procedures to stop the bleeding and fix bone.
"I feel a lot more confident and a lot more optimistic than I did two, three days ago", Sava said.
Two Capitol Police officers, David Bailey and Crystal Griner, and House Republican aide Zack Barth, were also injured in the shooting.
The hospital upgraded the third-ranking Republican leader from critical condition. "The doctor added, however, that Scalise will certainly be in the hospital for a considerable period of time, presumably weeks".