Hodgkinson, from IL, who had lashed out against United States president Donald Trump and other Republicans over social media, was killed by Mr Scalise's security detail and other police officers.
Scalise, 51, who represents a district in Louisiana and is the House majority whip, had previously been listed in critical condition. However, Sava said that the doctors "are encouraged by improvement in his condition" and "an excellent recovery is a good possibility".
The bullet struck Scalise in the hip, and traveled across his body, shattering bones and passing through internal organs, causing major internal bleeding.
Lobbyist Matt Mika was shot multiple times and critically injured and remained hospitalized.
President Donald Trump visited Scalise at the hospital Wednesday night and later said in a speech, "He's a great fighter and he's going to be OK, we hope".
Bailey was spotted Friday in the Capitol, on crutches and out of uniform, accepting congratulations from fellow officers.
At Friday's hospital news conference, Scalise's chief of staff Brett Horton read a statement from Jennifer Scalise, the congressman's wife.
U.S. Rep. Mo Brooks (R-AL) talks to reporters after a gunman opened fire on Republican members of Congress during a baseball practice near Washington in Alexandria, Virginia, U.S., June 14, 2017. His condition is critical, and he will require additional operations. The shooter was an IL man, James Hodgkinson, who had lashed out against President Donald Trump and Republicans over social media. The annual GOP-Democrats baseball game raises money for charity. "We are forever grateful for the heroism" of the officers, she said.
Authorities say they are examining a cell phone, a computer and a camera found inside a white van where the gunman who wounded a top Republican congressman and several others had been living.
The FBI said it was investigating the shooter's "activities and social media impressions" in the months leading up to the attack.