The statement from the hospital comes after President Trump, in an address from the White House, called Scalise a "fighter" and promised him the prayers of the nation and "frankly the entire world". The bullet travelled across his pelvis, fracturing bones, injuring internal organs, and causing severe bleeding.
He had been fielding at second base when he was hit, and dragged himself away from the infield, leaving a trail of blood until colleagues could rush to his aid.
Democrat and Republican lawmakers will meet tonight in a rare bipartisan exercise, even though they are literally playing hardball. They signed oversized cards for the wounded.
Hodgkinson, 66, of Belleville, Illinois, had campaigned for Bernie Sanders in November's presidential election and filled his Facebook page with screeds against Donald Trump and previous year against Hillary Clinton, the Democrat who won the nomination but lost the general election to Trump. He had a history of posting angry messages against Mr Trump and other Republicans on social media.
The gunman, 66-year-old James Hodgkinson of Belleville, Illinois, was wounded by Capitol Police and later died.
Following the shooting, there have been calls to end incendiary rhetoric in politics.
Democrats cautioned against falling into partisanship or apportioning blame. He said he hoped the game would help heal emotional wounds.
On Thursday, the hospital reiterated that Scalise will need more operations and will be in the hospital "for some time".
Scalise's wife, Jennifer, has been by his side, as Trump and others stopped by to pay visits.
For the game, which began in 1909, members of the Senate and House of Representatives donned uniforms representing teams from their constituencies for the game and many topped them with hats from Louisiana State University, Mr Scalise's alma mater, as a tribute. The popular and gregarious politician is known for his love of baseball and handed out commemorative bats when he secured the job of House whip several years ago.
Wounded NCCU alum throws out first pitch at Congressional Baseball Game
President Donald Trump praised Bailey and Griner in a video message that played before the start of the game. A lone gunman opened fire during the early morning on a group who were practicing on the field.
Rep. Roger Williams, a Texas Republican whom Barth works for, was also hospitalized and released with an injury to his leg.
FOX8's Alex Rose spoke with U.S. Rep. Mark Walker, a Greensboro Republican, about the GOP baseball practice shooting in Alexandria, Virginia Wednesday morning.
The running tally of results has Republicans and Democrats both at 39 wins, 39 losses and one tie.
But in another show of bipartisanship, Thursday night's congressional baseball game will go ahead as scheduled, in Nationals Park.
Thursday, the Federal Bureau of Investigation said both of Hodgkinson's firearms - a 9 mm handgun and 7.62 mm Chinese-made assault rifle - were purchased legally. Democratic former Alexandria Mayor Bill Euille said he had spoken often with the man on recent mornings at the nearby YMCA.
Hodgkinson belonged to multiple anti-Republican political groups and was upset about Trump's election victory, brother Michael Hodgkinson said. Authorities are investigating the incident but have not identified a motive.
The GOP lawmakers' team was taking batting practice when gunshots rang out and chaos erupted.
"When the leadership of this country is civil towards one another, maybe the public will start being civil towards one another too", said Rep. Mike Doyle, D-Penn., the Democratic manager.
The late night host has been very outspoken against the president ever since he took office.
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