MedStar Washington Hospital Center Director of Trauma Dr. Jack Sava leaves a news conference in Washington, Friday, June 16, 2017, about the condition of House Majority Whip Steve Scalise of La. who was shot in Alexandria, Va., Wednesday, June 14, 2017, during a congressional baseball practice.
A rifle bullet hit his left hip, shattering bones, tearing organs, and leaving him in a critical condition.
A list of names - including some Republican members of Congress - was found with the Alexandria shooter, according to a law enforcement source and Rep. Mo Brooks, who was on the list and present at the practice but unharmed by the shooting.
The hospital also said that Scalise had received "multiple units of blood transfusion" and that he would require additional operations.
The surgeon on Friday said he was "a lot more confident and optimistic" about Scalise's recovery than he was two days ago.
The doctors said that while Scalise remains in critical condition, they "are encouraged by improvement in his condition".
The annual charity game, a tradition since 1909, was held this year at Nationals Park in Washington, D.C.
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"By playing tonight, you are showing the world that we will not be intimidated by threats, acts of violence, or assaults on our democracy", Trump said.
They said that his "risk of death" has substantially lowered than when he arrived at the hospital.
"It's been much more hard than people even thought at the time", Trump told reporters at the White House on Thursday, adding he also visited the wounded Capitol Police officer at the hospital.
Hodgkinson died at the hospital Wednesday after he was shot by police. Griner is still hospitalized at MedStar and "in good spirits", Sava said.
More than 20,000 tickets had been sold for the game and it was on track to raise more than $1m, roughly double what it did previous year, for charities, its organisers said.
Mika is a lobbyist for Tyson Foods and a former aide to Michigan Republican Rep. Tim Walberg.
Scalise was reported to have been tended to by Rep. Brad Wenstrup of OH, a US Army Reserve doctor who served in Iraq, before his treatment at the hospital.
The Capitol Police Memorial Fund was added to the list of charities that will receive money raised by the game in honour of two members of Mr Scalise's security detail who were at the Wednesday practise session and returned fire.