The president also asked for prayers for lobbyist Matt Mika, also critically wounded during Wednesday's attack on Republican members of Congress who were attacked while practicing for an annual charity baseball game.
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Four people were wounded by gunfire and two sustained other injuries, authorities said.
The House of Representatives' No. 3 Republican leader was in grave condition when he was first shot.
Steve Scalise, the Republican congressman who was shot by a gunman during early-morning baseball practice on Wednesday, remains in a critical condition in hospital, as the investigation continues into the attack that left five people injured. "The game will go on".
From the stands, Vince Wetzel, a resident of Sacramento, California, who is visiting Washington and chose to take in the game, said, "It's just a good call to put aside political differences and just play some baseball".
The Illinois congressman grew emotional as he described seeing his colleague, Rep. Steve Scalise, lying motionless on the ground. "The lagniappe is the fact that so many people are calling asking for purple-and-gold garb and wanting to honor Steve and LSU".
"He remains in critical condition, but has improved in the last 24 hours", the hospital said. Scalise graduated from LSU in 1989 with a computer science degree and a minor in political science.
It's also an opportunity for Republicans and Democrats to get off the floor and onto the field for a friendly competition that raises money for charity. Moments before, the crowd broke into a chant of "USA".
During the game, a special tribute was held for Scalise, who is being treated at Medstar Washington Hospital Center.
Investigators say they still do not know if the shooter James T. Hodgkinson had an attack plan. "We're here to show solidarity". New Orleans Mayor Mitch Landrieu wore an LSU jersey to the game to support Scalise.
Addressing Scalise, Rep. John Lewis, D-Ga., said, "You are not alone". "We understand he is lucky to be alive and we owe it to these wonderful individuals and Matt's fighting spirit and grit. It's important to reflect".
Almost every year for more than 100 years, members of Congress from both parties face off in a friendly, but competitive, baseball game. Proceeds for the game benefit a number of local charities.
Fans attending the game are also planning to use the opportunity to stress bipartisan love.
Asked if he thought the day's events should bring about any change in gun laws, or if negative campaigning in last year's presidential campaign or in his own congressional races are at fault, Davis said that given the tragedy of the day, "I just don't think it's the right time to ask those questions". "I'm prayerful he will pull through, and I hope he does", he said.
Hodgkinson was also a one-time volunteer for Bernie Sanders' campaign for president past year.
Vice President Mike Pence said Thursday, "We're especially grateful to the fearless police officers who ran into danger without regard to their personal safety ... and prevented an even greater tragedy".
In his first public comments since the shooting, Dr. Jack Sava of MedStar Washington Hospital Center said it's a "good possibility" that the Louisiana Republican will be able to return to work in his full capacity. The Castro government is certain to reject Trump's list of demands, which includes releasing political prisoners, halting what the US says is abuse of dissidents and allowing greater freedom of expression.