The bullet entered his left hip and tore through his pelvis, breaking bones, injuring organs and causing severe bleeding.
Scalise underwent his third surgery Thursday, which was anticipated when he first came into the hospital.
Louisiana member Mr Scalise, 51, was one of five people shot when gunman James Hodgkinson opened fire as the Republican team practised for a charity game against Democrats in Alexandria, Virginia, on Wednesday. He died after officers in Scalise's security detail and local police fired at him.
The game Thursday, a Washington tradition since 1909 in which Republicans and play Democrats, went on Thursday evening at Nationals Stadium, home of the city's major league baseball team. Investigators are trying to determine what his intent may have been - whether it was a list of potential targets for violence or whether he wrote them down for some other reason, one official said.
Sen. Jeff Flake of Arizona, who was at Wednesday's practice and gave medical help after the shooting, said it would have "been awful" if the game had been canceled, and said Scalise would want it to go on.
Earlier Friday, House Speaker Paul Ryan paid a visit to his injured colleague, who faces the prospect of a lengthy hospitalization after getting shot in the hip at a baseball practice by a deranged man with grudges against Trump and the GOP.
"I purchased my ticket a few weeks ago, but with what happened yesterday, it has more meaning to me today", said D.C. resident Amanda Linton.
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Scalise has remained under sedation, although doctors have lightened the medication at times so that the congressman can communicate with relatives. "That is the source of unity, and more than ever, we must embrace it", the president said. Infection remains a considerable risk in the days and weeks during Scalise's extended hospital stay, Sava said.
"Most of us would not even think to consider that a benign wound", Sava said.
The FBI said it was investigating the shooter's "activities and social media impressions" in the months leading up to the attack. The shooter was an IL man, James Hodgkinson, who had lashed out against President Donald Trump and Republicans over social media.
Hodgkinson contacted both of his state's Democratic senators frequently, always through email links on their websites, spokesmen said Friday.
He's also saluting the Capitol police officers injured in the attack on a Republican Congressional baseball practice. Griner remains hospitalized at MedStar Hospital after getting shot in the ankle, and Sava described her in good condition.
"We continue to hold all of those wounded and fighting for recovery in our hearts and prayers, including Matt Mika, who was also badly wounded", he added.