Sen. John Hoeven said, "Our thoughts are with House Whip Steve Scalise, our Capitol Police officers and congressional aides who were injured in today's shooting while practicing for a charity baseball game".
Mr. Scalise was shot in the hip, his office said, adding that the Republican's condition was stable.
The hospital where Scalise is recovering after being shot said the congressman remains in critical condition and will require several more operations.
Brooks said he got a look at the gunman and described him as a white male who was "a bit on the chubby side".
Hodgkinson, 66, who was shot by police at the scene and later died, was a member of a group called Terminate The Republican Party and had volunteered for the presidential campaign of Democratic candidate Bernie Sanders a year ago.
Hodgkinson, who had been living in his van in Alexandria for the past few months, had posted anti-Trump rhetoric on his Facebook page and had written letters to his hometown newspaper blaming Republicans for what he considered an agenda favoring the wealthy.
A shooting in Alexandria leaves a Congressman in critical condition and several others hurt.
After an all-members briefing where Democrats and Republicans held hands and prayed, House Speaker Paul Ryan and top Democrat Nancy Pelosi addressed the somber chamber and proclaimed lawmakers were "united".
Shimkus has visited Scalise in the hospital, but didn't stay long because he didn't want to be "in the way".
Like most members of Congress, Newhouse does not have a personal security detail and doesn't foresee himself getting one. The game will be played tonight at Nationals Park as planned. In an earlier announcement from the White House, Trump also praised the "heroic actions" of the Capitol Police officers who stopped the shooter in his tracks.
"We're going to look over our shoulder a little bit", she said.
The gunman was wounded when police returned fire, and he later died.
"Any attack on members of Congress is an attack on our democracy".
The president had a message for the Scalise family: The entire country "sends its love".
Lipinski said he talked with Republican congressmen who were at the baseball field, some of whom were standing between Scalise and the shooter.