Representative Steve Scalise, who was critically injured last month by a gunman who opened fire at a congressional baseball practice, was readmitted on Wednesday to a Washington hospital’s intensive care unit over concerns about infection, his office announced.

The condition of Mr. Scalise, 51, who has been hospitalized at MedStar Washington Hospital Center since the shooting on June 14, was also downgraded to serious from fair. The hospital said in a statement that Mr. Scalise faced “new concerns for infection,” but it did not detail those concerns.

The hospital said it would provide another update on Thursday.

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Mr. Scalise has undergone several surgeries and was moved out of the intensive care unit on June 22. Of the four people shot at the baseball field in Virginia, he was the most seriously wounded. A bullet entered his left hip, shattering bones and ripping through organs and blood vessels, doctors said. The gunman was killed in a shootout with the police.

Wednesday’s news was the first update provided about Mr. Scalise’s condition since June 23, when his staff announced on Twitter that he was improving and undergoing “an extensive period of healing and rehabilitation.” In the days after the shooting, doctors worked to control internal bleeding and prepare him for operations to repair abdominal injuries.

Doctors said in mid-June that they were unable to predict how long Mr. Scalise, who is from Louisiana and is the No. 3 Republican in the House, would remain in the hospital.

A stream of well-wishers, including President Trump, have visited him. Representative John Shimkus of Illinois, who shares a home with Mr. Scalise and two other representatives near the Capitol, said last month that he realized during a hospital visit that Mr. Scalise’s wounds were far more serious than he initially thought.

“It’s going to be a tough rest of the year for us,” Mr. Shimkus said.