The shooter is identified as James T. Hodgkinson, 66, of Belleville, Illinois.
"We have no intention to remove all bullet fragments at this point", he said, noting that is common because finding and removing that many fragments is more risky than leaving them inside the body.
Wednesday's shooting sent shock waves through Washington, where most members travel without a personal security detail.
The hospital also said that Scalise had received "multiple units of blood transfusion" and that he would require additional operations.
"Had a chance to talk to him about his priorities, had a chance to talk to him about his family, had a chance to talk to him about that fact that he was gonna be playing in this baseball game", Neal said.
Mr Scalise, the House Majority Whip, remains in a critical condition in hospital.
Scalise and three other people were shot early Wednesday at a park in suburban Washington as they practiced for a congressional charity baseball game.
"While the president would like to attend the game and show his support for all of these courageous public servants, he has been advised that there is not enough time to follow Secret Service protocols", Trump spokesman Sean Spicer said Wednesday night.
Scalise's condition improves, but more operations and long hospital stay expected
The US Capitol Police and representatives for the three lawmakers did not immediately respond to requests for comment. Hodgkinson had a history of posting angry messages against Mr Trump and other Republicans on social media.
"It's been much more hard than people even thought at the time". Scalise, a veteran Louisiana politician, was reported by CNN to be clinging to life after surgery.
"He underwent immediate surgery, and an additional procedure to stop bleeding", the statement said. "So we all owe Steve a big, big thank you".
House Speaker Paul Ryan, R-Wis., paid a visit to his injured colleague at the hospital Friday. According to Hodgkinson's social-media history and other reports, he expressed broad dissent against Trump and Republican policies. The offices of both senators - Dick Durbin and Tammy Duckworth - turned over the emails to Capitol Police and declined to offer specifics about their content.
There was a loud ovation when Special Agent David Bailey, one of the Capitol Police officers injured in the attack, threw out the first pitch. The hospital also said it will continue to provide periodical updates.
Rep. Steve Scalise is still in critical condition, but his health is improving, the Congressman's surgeon said two days after Scalise was shot at a practice for the Congressional Baseball Game.
So far, investigators have not linked Hodgkinson to any radical groups, said a law enforcement official who spoke on condition of anonymity because the official was not authorized to discuss the investigation publicly.
Ms Griner remains in hospitali at MedStar after being shot in the ankle and Mr B ailey was spotted on Friday in the Capitol, on crutches and out of uniform, accepting congratulations from fellow officers.
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