Scalise was shot Wednesday morning as a gunman sprayed bullets into a GOP congressional baseball practice. The congressman underwent another surgery Saturday, and the hospital says he is more responsive and speaking with family.
The gunman, identified by officials as James Hodgkinson, died after the shootout.
"I hope he's in good enough shape to watch, because he'll certainly feel good about what he sees", Flake said.
The congressional game, which dates to 1909 and is a summertime tradition on Capitol Hill, is a rare example of bipartisanship in an increasingly polarized Washington.
Medstar Washington Hospital Center released the update on behalf of the Scalise family.
Doctors at MedStar Washington Hospital, where Rep. Scalise is being treated, discussed his condition on Friday saying that they believed he would be in the hospital for a considerable amount of time, possibly weeks.
Wounded U.S. Capitol Police officer David Bailey set aside one of his crutches and threw out the game's first pitch.
"They saved the lives of our members of Congress and prevented that dark day from becoming a tragedy beyond imagination". He has undergone several surgeries and has more ahead.More news: Iran launches missiles into eastern Syria - KXLF.com | Continuous News | Butte, Montana
Hodgkinson - an IL 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.
"We are encouraged in the improvement in his condition in the last 36 hours". Lobbyist Matt Mika was shot multiple times and critically injured and remained hospitalized.
Congressional aide Zach Barth was the fourth person hit and is also expected to make a full recovery, NPR's Vanessa Romo reports.
"There is so much you do that I disagree with", House Financial Services Committee Chairman Jeb Hensarling, R-Texas, a staunch conservative, told his panel's top Democrat, unwavering liberal Rep. Maxine Waters, D-Calif.
"I was there last night", he said. Both had appeared on the House floor earlier Thursday. However, members said the shooting served as the best motivator for both parties to come together and play ball.
But Flake said the final score wasn't likely to matter this year.
The game raised more than $1 million for the Boys and Girls Club of Greater Washington, Washington Literacy Center, the Washington Nationals Dream Foundation and the Capitol Police Memorial Fund in honor of those injured in the line of duty during Wednesday's shooting.
Still, finger-pointing lingered as some on each side suggested the other had contributed more to the disparaging broadsides they've increasingly aimed at each other.