Scalise's condition was upgraded to "serious", from "critical" after undergoing another surgery on Saturday, according to a statement from Dr. Jack Sava, the director of trauma at the MedStar Washington Hospital Center.
Sava declined to put a timeline on when that would happen or when Scalise, 51, would be able to leave the hospital.
The AP said many of those who played wore LSU hats to honor Scalise, who graduated from the university.
Hospital officials previously said Scalise would need multiple operations and weeks to recover after a bullet tore through his pelvis, fracturing bones, injuring internal organs and causing severe bleeding.
"We have controlled the internal bleeding and his vital signs have stabilized", Sava said during a news conference.
His family said they appreciate the support they've received from lawmakers and the president, and are thankful for the bravery of the special agents.
Hodgkinson was fatally shot during an exchange on gunfire with police during the rampage.
The shooter was identified as James T. Hodgkinson, a 66-year-old home inspector from IL who had several minor run-ins with the law in recent years and belonged to a Facebook group called "Terminate the Republican Party".
"We have no intention to remove all bullet fragments at this point", he said, noting that is common because finding and removing that many fragments is more risky than leaving them inside the body.
Scalise should be able to walk again, Sava said. But he will remain in the hospital for "a considerable period of time" and faces additional operations.
Even with the progress over the last two days, though, Sava said Scalise will remain in the hospital for the near future.
Sava added that Scalise's "risk of death right now is substantially lower" than it was early Wednesday, when he was shot on a baseball field in Alexandria, Va., as he practiced with other Republican lawmakers.
Moments before, Bailey stood in the middle of Democratic and Republican players who each took turns hugging him tightly and thanking him for protecting one of their own, House Majority Whip Steve Scalise, R-La. Griner remains hospitalised at Washington's MedStar Hospital after getting shot in the ankle, and Sava described her in good condition.
Bailey was spotted Friday in the Capitol, on crutches and out of uniform, accepting congratulations from fellow officers.
Ticket sales picked up after Wednesday's shooting, eventually setting an attendance record, the organizers said, as attendees such as Alexander Hilten, 16, of Arlington, Virginia, made a decision to come to the game for the first time.