Doctors immediately performed surgery, but additional operations will be required, the hospital said in the late-night statement.
Steve Scalise, who was shot in the left hip, had surgery Thursday related to his internal injuries and a broken bone in his leg. Sava didn't address what organs were damaged.
A shooter, killed by return fire from officers, sprayed rifle fire at congressional Republicans practicing on a diamond in Alexandria, Virginia, a Washington suburb.
"The Scalise family greatly appreciates the outpouring of thoughts and prayers", MedStar Washington Hospital Center said in a statement released on behalf of his kin, reports CNN.
"He will certainly be in the hospital for a considerable period of time", he said.
Crystal Griner, one of the responding Capitol Police Officers, was shot in the ankle.
Pakistan secures ICC final berth
Pakistan cruised to a victory and a place in the final after bowling England out for 211 on a worn pitch in Cardiff . If this becomes a trend, England will start to develop a reputation, but I believe we are some way from that.
Jennifer Scalise also is thanking the first responders who rushed to her husband's aid Wednesday and the staff at MedStar Washington Hospital Center, where her husband remains in critical condition.
The person did not disclose the names, but said those listed had been briefed. The President also credited Scalise for bringing unity to the country. Scalise has undergone number surgeries so far, and his recovery is expected to be lengthy. He was shot in the hip but the bullet tore through his pelvis and injured internal organs.
Trump's comments came at the beginning of his speech in Miami Friday announcing a partial rollback of ties to Cuba - reversing changes made by President Barack Obama's administration.
House Speaker Paul Ryan visited Scalise at the hospital Friday, an aide said.
Scalise was fielding ground balls at second base when he was shot at a practice for the annual Republicans-Democrats baseball game.