"He is more responsive, and is speaking with his loved ones", the hospital said, adding that he had been downgraded to "serious" condition.
A congressman said Hodgkinson asked him whether it was the Democratic or Republican team practicing before he carried out the shooting. Doctors said his prognosis was positive on Friday.
Scalise, facing "an imminent risk of death", was rushed to the hospital in a helicopter.
The hospital released the statement on behalf of Scalise's family.
Witnesses at the baseball field said Hodgkinson asked a local resident about the party affiliation of the congressmen; a few moments after he learned they were Republicans, he produced a semiautomatic rifle and began firing volleys of shots.
Lobbyist Matt Mika was shot multiple times and critically injured and remained hospitalized.
Sava said Friday that there are hundreds of bullet fragments in Scalise's body, but 'we have no intention to try and remove all the bullet fragments at this point'. The president made his comments as he spoke in Miami to announce a new policy on Cuba. He has required surgery several times since the shooting.
The hospital said Scalise underwent another surgery Saturday to treat the gunshot wound.
Police and Federal Bureau of Investigation officials declined to confirm media accounts that the list of names Hodgkinson carried was a "kill list"; they said the names were listed without any other comment. They also said "we continue to be grateful beyond words for the heroic actions of the U.S. Capitol Police this week".
Hodgkinson, a Belleville, Illinois, home inspector who had been living out of his van near the park, had a social media page filled with criticism of Republicans and the Trump administration.
The man who shot Scalise and others at the baseball practise had with him a piece of paper with doodles and the names of three lawmakers, according to a person familiar with the case. "He underwent another surgery today, but continues to show signs of improvement".
House Speaker Paul Ryan, R-Wis., paid a visit to his injured colleague at the hospital Friday.