Standing at second base, Mr. Scalise was struck once in the left hip, according to witnesses, and collapsed as the shots rang out, one after another, from behind a chain-link fence near the third-base dugout. Witnesses said Mr. Scalise, of Louisiana, “army crawled” from the infield to the grass as the shooting continued.

His injuries are extensive, and he was in critical condition Wednesday night, MedStar Washington Hospital Center said in a statement. As the bullet traveled across his body, it broke bones, tore up internal organs and caused major internal bleeding.

Doctors operated immediately, but additional surgery is required, the hospital said.

Mr. Trump and his wife, Melania, made a trip to the hospital on Wednesday night, arriving with two large bouquets of white flowers. The president sat privately with Mr. Scalise, and spoke with his doctors and wife, Jennifer, for about 15 minutes. He also briefly chatted with Capitol Police officers there before returning to the White House.

“Just left hospital,” Mr. Trump tweeted. “Rep. Steve Scalise, one of the truly great people, is in very tough shape - but he is a real fighter. Pray for Steve!”

Image Steve Scalise, the majority whip of the House of Representatives. Credit... Gabriella Demczuk for The New York Times

Local officers arrived at the Alexandria ball field minutes after they received desperate calls for help, including calls from those still under siege at the field, the authorities said. The F.B.I. said it would take the lead in the investigation, treating it as an assault on a federal officer.



Tim Slater, special agent in charge of the bureau’s Washington field office, said that investigators were “exploring all angles” but that he could not comment on a motive. Asked whether the shooting was an assassination attempt, he said it was “too early in the investigation to say one way or another.”

The F.B.I. said Mr. Hodgkinson had a handgun and a rifle, which he bought in March, according to a law enforcement official. Witnesses described a man with white hair and a beard wielding a long gun as he stood behind the dugout.

“He was hunting us at that point,” said Representative Mike Bishop, Republican of Michigan, who was standing at home plate when the shooting began.