Earlier there were reports that the suspected shooter was among the five people transported to an area hospital.
Kyrsten Sinema: "So grateful for Capitol Police, who saved lives this morning at congressional baseball practice".
"Scalise hit. Other staffers hit", Fox News reporter Chad Pergram tweeted on Wednesday just before 8 a.m.
Barton, the team manager, said he took cover behind a dugout when the shooting started.
"I hear loud explosions".
She said the shooting went on for "quite a while".
Late Wednesday morning, Trump said Hodgkinson had died of his injuries. He said he grabbed Scalise's phone to call his wife.
In a dramatic blow-by-blow account, Representative Mo Brooks of Alabama told CNN the gunman was armed with a rifle and appeared to be a white male, "a little bit on the chubby side".
Both officers engaged the shooter with their sidearms, commanding him to drop his weapon as they returned fire. Williams says Barth is doing well and is expected to make a full recovery.
Rep. Jeff Duncan, R-Sc., and Rep. Ron Desantis, R-Fl., were getting into Duncan's vehicle when the man asked them about the political affiliation.
"Please take a moment today to cherish those you love, and always remember those who serve and keep us safe", Trump said. House Speaker Paul Ryan also identified two members of the Capitol Police who were injured, Krystal Griner and David Bailey.
Rep. Dave Brat, R-Va., said this incident points to the need for more security for congressional members, especially in light of the amount of angry people at town halls lately.