Scalise underwent a third surgery Thursday and was still in critical condition in the morning at a local Washington, D.C., hospital.
The congressman grievously wounded when a gunman opened fire at a Republican baseball practice is delivering a Father's Day message through his Twitter account.
House Majority Whip Rep. Steve Scalise was the only congressman injured in the shooting.
Trump, in Miami Friday afternoon delivering remarks on Cuba policy changes, said of Scalise, "Because of him and the tremendous pain and suffering he's now enduring - he's having a hard time, far worse than anybody thought - our country will perhaps become closer, more unified".
Dr. Jack Sava, director of trauma at Medstar Washington Hospital, told reporters that multiple surgeries appeared to have brought multiple internal hemorrhages under control.
Sava estimates there are hundreds of bullet fragments in Scalise's pelvis and says doctors don't intend to try to remove them all, as that could cause more harm than good. Lawmakers called for a new dialogue on lowering the partisan temperature, and Trump urged Americans to come together as he assumed the role of national unifier for one of the first times in his presidency.
Republican and Democrat members of Congress kneeled at the second base and prayed in a touching dedication to Rep. Steve Scalise (R-La.) during their annual charity baseball game.
Hodgkinson contacted both of his state's Democratic senators frequently, always through email links on their websites, spokesmen said Friday.
The FBI said it had processed a white conversion van owned by Hodgkinson, which was parked at the YMCA adjacent to where the shooting happened. He added that Scalise would be in the hospital "for some time" and would need "a period of healing and rehabilitation" after being discharged.
He also said that Officer Crystal Griner, who was shot in the ankle, is in "good condition". According to the medical staff, Scalise arrived in critical condition with a "imminent risk of death".
Lobbyist Matt Mika was shot in the chest at the baseball practice.
But Flake said the final score wasn't likely to matter this year.
Shortly after the shooting, Bernie Sanders, the former candidate for the Democratic presidential nomination, said on the Senate floor that the shooter apparently was a volunteer for his campaign previous year.
The game at Nationals Park carried on a century-old bipartisan ritual, this one tinged with worry about Louisiana Rep. Steve Scalise and the players' determination to answer the attack by coming together in sport.