The shooter died in a hospital after exchanging fire with police.
The Alexandria Police Department is tweeting that they have the suspect in custody but are asking people to stay away from the area.
No other members of Congress were shot.
Four others were wounded: a congressional aide, a lobbyist for Tyson Foods, and two US Capitol Police officers.
FBI Agent Tim Slater would not characterize the attack, saying "We are exploring all angles".
Lawmakers noted their good fortune in having armed protectors on hand - "Thank God", they exclaimed over and over - and said otherwise the shooter would have been able to take a huge deadly toll.
Hugo Lloris sera titulaire contre l'Angleterre
On sait qu'à l'avenir il continuera à nous sauver et à nous faire gagner des matches", a ajouté le défenseur central. Je ne pense pas que "frustration" soit le mot juste le concernant.
They were in good spirits despite the heat and humidity as they prepared for the congressional baseball match that pits Republicans against Democrats. "In the field, I see Representative Scalise is shot but moving and he's trying to drag himself through the dirt out into the outfield".
The year 2017 is just 165 days old, yet it already has suffered 154 mass shootings in America - almost one per day - according to the Gun Violence Archive, which defines a mass shooting as one in which four or more victims are hit, not including the shooter. The man calmly asked which party's lawmakers were practicing and Duncan told him they were the Republicans. And having no self-defense, the field was basically a killing field. He tells them that they went to Iowa to campaign for Senator Bernie Sanders's presidential campaign.
While Deal cautioned against presuming the motivations of the shooting were political, he said that the political environment today is such that "anyone in elected office is always subject to being attacked, and we all know that", he said. "I'm in the dugout, I see a staffer who's got a leg wound".
GOP shortstop Rep. Ryan Costello, wearing a Reading Fightin Phils uniform, throws to third base for an out on base runner Rep. Ed Perlmutter during the Congressional Baseball Game at Nationals Stadium in Washington on Thursday, June 23, 2016.
Scalise was in critical condition after suffering damage to internal organs, and his injuries will require additional operations, according to a MedStar Washington Hospital Center medical update late Wednesday.
Gabrielle Giffords, the former Arizona lawmaker shot during a 2011 assassination attempt, on Wednesday said her "heart is with my former colleagues, their families & staff, and the U.S. Capitol Police - public servants and heroes today and every day".
Before becoming majority whip, Scalise was chairman of the conservative Republican Study Committee, which includes more than 170 conservative lawmakers.
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