The FBI has taken control of the investigation.
A rifle-wielding gunman, identified as IL man James.
Brooks also said the shooter shot two officers working protective detail for the Congress members at the event.
Sen. Flake, of Arizona, said he took cover in the dugout as the gunman and law enforcement exchanged fire. The 2006 case was dismissed after the alleged victim didn't show up for the court hearing.
Although the practice was taking place in Alexandria, Va., across the Potomac River from the Capitol, police were on hand to protect Rep. Scalise, the majority whip and No. 3 Republican in the House of Representatives.
Susan Griffiths, spokeswoman for George Washington University Hospital Center, said two people were being treated there and were in critical condition. I see a rifle. and I see a little bit of a body.
Authorities say the Capitol Police officers returned fire with the gunman before local police arrived shortly after 7 a.m.
Praising the actions of law enforcement officers and first responders, Trump said the suspected assailant - identified as James T. Hodgkinson, 66, of Belleville, Ill.
"Our fearless Capitol Police perform a challenging job with incredible skill and their sacrifice makes democracy possible", Trump said.
"Finally, the shooter was shot behind home plate as he was circling around to the first base dugout where there were a number of USA congressmen and other folks", Rep. Mo Brooks, R-Ala., told FMTALK1065.
"Please join me in praying for quick healing for Steve, the police officers, and the Congressional aide who were injured". Formerly with the U.S. Fish and Wildlife Service, Bailey was praised by House Speaker Paul Ryan for his heroic efforts.
Iran arrests seven suspects linked to Tehran attacks
Tehran police said the vehicle the attackers used for both attacks was discovered on Saturday in the city center. Alavi also said that in the past three months, Iran has broken up 25 terrorist teams.
"He was hunting us at that point", said Rep. Mike Bishop of MI.
"I just didn't want her to wake up and learn the news", Flake said.
Scalise is stable and is expected to make a full recovery.
The police added on Twitter that the suspect was in custody, and asked people to stay away from the area to let emergency vehicles pass through.
Senator Lamar Alexander's office also said he is safe and wasn't at practice.
"Prior to entering surgery, the Whip was in good spirits and spoke to his wife by phone", his office said. Sources identify the staffer as Zachary Barth, a legislative correspondent for Rep. Williams.
When Scalise was shot he went down on the infield between first and second base, then dragged himself into the grassy outfield as the incident unfolded, leaving a trail of blood, Brooks said.
Scalise was shot in Alexandria, Virginia, where members of Congress were attending a practice for the GOP congressional baseball team.