Scalise is a member of the team and had been fielding balls at second base in preparation for the game when he was shot.
Earlier Thursday, Republican lawmakers met behind closed doors to share reflections and pray. They signed oversized cards for the wounded.
"You see some of the evidence about the shooter coming out and his politics - his politics were his religion", Davis said of 66-year-old James T. Hodgkinson of Belleville.
Over social media he had lashed out at Mr Trump and the GOP.
Capitol Police officers in Scalise's security detail returned fire, and Hodgkinson later died from his injuries.
Some Republican lawmakers blamed the shooting on vitriolic political rhetoric, particularly rising from the left in the era of Trump.
Democrats cautioned against falling into partisanship or laying blame.
Rep. Steve Scalise is improving but is still in critical condition, according to an update from his doctors.
President Trump paid a visit to Scalise Wednesday night, meeting with his family and sitting by the congressman's bedside.
As Scalise struggles to recover, House Speaker Paul Ryan and Minority Leader Nancy Pelosi conducted their first joint interview during Thursday's Congressional Baseball Game.
After the hospital visit, Pence headed to Miami for a conference on Central America and meetings with the leaders of El Salvador, Honduras and Guatemala. Capitol police officers were also seriously injured along with a current and former congressional aide.
Nikkei falls after weak USA data overshadows Fed hike; financials underperform
Also on Wednesday, a prominent Republican was among those shot by a gunman said to be angry with Trump. The euro was down 0.3 percent at $1.1183, a six-day low, while the yen was flat at 109.58 per dollar.
Lobbyist Matt Mika was shot multiple times and remains hospitalized.
The shooting occurred at a popular park and baseball complex in Alexandria, Virginia, across the Potomac River from Washington, where Republican lawmakers and others were gathered for a morning practice about 7 a.m.
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.
Authorities also were going over a mobile phone, computer and camera taken from Hodgkinson's white van, which was parked near the ballfield.
He said he talked with Republican team manager Joe Barton of Texas after the shooting and they agreed that that "we shouldn't let incidents like this or people like this change our routine or how we live our lives".
The GOP lawmakers' team was taking batting practice when gunshots rang out and chaos erupted. After Scalise was shot in the hip, the bullet traveled through his pelvis, fractured bones and injured internal organs. Rep. Mo Brooks, an Alabama Republican, said his colleague "crawled into the outfield, leaving a trail of blood". "We are all praying for those who are attacked and for their families", he said.
The gunman had a rifle and "a lot of ammo", said Sen. Jeff Flake of Arizona, who was at the practice. "And I think what happened yesterday was symptomatic of it", Republican Representative Mark Sanford told MSNBC on Thursday.
Rep. Jeff Duncan of SC said he had just left the practice and encountered the apparent gunman in the parking lot before the shooting.
Each member of Congress was introduced Thursday night, garnering hoots and hollers from the crowd as they cheered on their favorite players. Some have suggested using federal money to provide security cameras in their offices, while others spoke of a need for protection when groups of them appear in public.
The president, whose administration has been dogged by allegations of ties between his 2016 campaign and Russian Federation, later wrote two tweets suggesting that Democrat Hillary Clinton, whom he defeated in last November's election, should be under investigation instead of him.
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