Separately, Republicans also met behind closed doors before leaving Washington for the week. They signed oversized cards for the wounded.
Over social media he had lashed out at Mr Trump and the GOP.
Speaking on the House floor, Representative Glenn Thompson issued a call to "replace the hateful rhetoric and resistance with respect".
But Scalise can hope to make an "excellent recovery", his trauma surgeon said Friday.
"Congressman Scalise is a good man, he's a principled leader and a patriot", Pence said.
On Wednesday night, Trump, accompanied by first lady Melania Trump, visited Scalise at the hospital.
Trump and his wife, Melania, visited with Scalise late Wednesday.
Zack Barth, an aide to Texas Rep. Roger Williams, was also shot but was treated and released from a hospital.
The deciding factor will probably be Rep. Cedric Richmond, D-La., who may be the best to have ever played in the game. Two lawmakers who were leaving practice when they encountered Hodgkinson before the shooting believe he was targeting Republicans. They were in good spirits despite the heat and humidity as they prepared for the congressional baseball match that pits Republicans against Democrats.
While the game provides some relief and bipartisanship in a town dominated by faction and division, the other more important aspect of the game has to do with how it benefits various charities.
It has emerged that Hodgkinson had been staying in the Alexandria area since March, where he had been living out of a white van.
A list of Republican lawmakers was found on Hodgkinson's body, CBS News reported, citing an unidentified USA official.
The GOP lawmakers' team was taking batting practice when gunshots rang out and chaos erupted.
Scalise was fielding ground balls at second base Wednesday when he was shot at a practice for the annual Republicans-Democrats baseball game. Rep. Mo Brooks, an Alabama Republican, said his colleague "crawled into the outfield, leaving a trail of blood".
"We will not give in to fear, violence or hate", Aguilar said. Jeff Flake said Mika was the most seriously injured.
"That's a tragic scene I'll never forget - of my friend laying on that field motionless", Davis said.
Rep. Jeff Duncan of SC said he had just left the practice and encountered the apparent gunman in the parking lot before the shooting.
The shooting prompted talk of improving security for lawmakers, most of whom are unaccompanied by officers in their normal day-to-day pursuits. He died after officers in Scalise's security detail and local police fired at him.
The question now is can the unity last after the Democrats routed the Republicans by a final score of 11-2. Gabby Giffords of Arizona was hit in the head and grievously injured while meeting with constituents at a supermarket parking lot in 2011.