Washington (CNN) Rep. Steve Scalise , a congressional staffer, a lobbyist and a member of the Capitol police force were shot Wednesday in Alexandria, Virginia, during a Republicans' early-morning practice ahead of a charity baseball game.

Federal law enforcement officials identified the alleged shooter as James Hodgkinson, 66, of Belleville, Illinois , who died following a shootout with authorities.

At least six people including Scalise, the third ranking member of House Republican leadership as the majority whip, were hospitalized.

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.

"Congressman Steve Scalise sustained a single rifle shot to the left hip. The bullet traveled across his pelvis, fracturing bones, injuring internal organs, and causing severe bleeding," MedStar said in a statement put out by Scalise's office. "He underwent immediate surgery, and an additional procedure to stop bleeding. He has received multiple units of blood transfusion. His condition is critical, and he will require additional operations. We will provide periodic updates."

A congressional staffer, Zach Barth, was also shot in the leg and has since been released from the hospital. Matt Mika, a lobbyist for Tyson Foods and former congressional staffer, was also identified as one of those shot. He was out of surgery and in critical condition as of Wednesday afternoon, his family said in a statement.

House Speaker Paul Ryan said two members of the Capitol Police -- Crystal Griner and David Bailey -- were injured Wednesday.

In a statement, Capitol Police said Griner was in "good condition in the hospital having been shot in the ankle," and Bailey "was treated and released having sustained a minor injury during the incident."

Trump made a surprise visit to MedStar Washington Hospital Center around sunset Wednesday.

He sat next to Scalise's bed and spoke with the congressman's family, according to White House press secretary Sean Spicer. He also spoke with Griner and her wife, as well as hospital doctors.

A senior administration official said the mood inside the hospital was somber during Trump's visit, which came hours after Scalise emerged from surgery still in critical condition after suffering a single rifle shot to his hip.

Rep. Roger Williams, a Texas Republican whom Barth works for, was also hospitalized and released with an injury to his leg.

Lawmakers described a chaotic scene during the shooting. Many members of the congressional GOP baseball team were huddled in a dugout while Capitol police -- who were part of Scalise's security detail -- and local Alexandria police engaged in a shootout with Hodgkinson. Congressional and law enforcement sources described it as a "deliberate attack."

Traces were still being done on the two firearms recovered at the scene -- an SKS rifle and a 9 mm pistol on Wednesday, a law enforcement source tells CNN.

House Republican and Democratic leaders called for unity, while President Donald Trump said in an address from the White House that the prayers of the nation and world are with Scalise.

"Congressman Scalise is a friend, and a very good friend," Trump said. "He's a patriot. And he's a fighter. He will recover from this assault -- and Steve, I want you to know that you have the prayers not only of the entire city behind you, but of an entire nation, and frankly the entire world. America is praying for you and America is praying for all of the victims of this terrible shooting."

"We are united. We are united in our shock. We are united in our anguish. An attack on one of us is an attack on all of us," Ryan said, drawing a bipartisan standing ovation.

Members practicing for traditional baseball game

Members of Congress were practicing for a charity baseball game that was scheduled for Thursday night at Nationals Park. Rep. Martha McSally, R-Arizona, said the game will still go on as scheduled. The annual game has been played since 1909, and McSally said lawmakers applauded the announcement at an all-members meeting.

Rep. Joe Barton, who manages the Republican team, told reporters that the Fallen Officers Fund has been added to the charities that will receive the proceeds.

Rep. Mike Doyle, who manages the Democratic team, said at the same conference that his team would host the Republican team at the Democratic club for dinner to reflect Wednesday.

"Some of them have probably never set foot in that building," he joked.

Lawmakers describe a terrifying scene

Lawmakers who spoke at the scene to reporters described a normal morning practice taking place at a field where they've practiced for years, when suddenly shots rang out. Lawmakers, staff members and even the young son of one of the members ran for cover, jumping into dugouts and over fences to avoid the gunshots.

Members described Scalise dragging himself roughly 15 yards away from second base, where he had been playing, and lying there until the shooter was neutralized, at which point some of them ran to assist him until he could be evacuated. Once they were able, Sen. Jeff Flake said he and Rep. Brad Wenstrup, who is a physician, went to where Scalise was lying to apply pressure to the wound. Scalise was coherent the whole time, Flake said.

Kentucky Sen. Rand Paul told CNN "it would have been a massacre" without the Capitol Police officers present.

"Nobody would have survived without the Capitol Hill police," Paul said on CNN. "It would have been a massacre without them."

"We had nothing but baseball bats to fight back against a rifle with," Alabama Rep. Mo Brooks said.

Flake added that he saw a member of Scalise's security detail return fire on the gunman for what felt like 10 minutes, even though the police officer was wounded in the leg.

"Fifty (shots) would be an understatement, I'm quite sure," Flake said when asked about the total amount of gunfire, including police returning fire.

Brooks said the shooter was behind the third base dugout and didn't say anything.

Shooter identified

Hodgkinson's Facebook page is largely political, and his profile picture is a caricature of Bernie Sanders as Uncle Sam.

The Facebook feed is filled with anti-Trump sentiments such as "Trump is guilty and should go to prison for treason."

He also "liked" a political cartoon that suggested that Scalise should be fired. On March 22, he posted "Trump is a Traitor. Trump Has Destroyed Our Democracy. It's Time to Destroy Trump & Co."

Vermont Sen. Bernie Sanders said both in a statement and on the Senate floor that he had learned the shooter had volunteered on his Democratic presidential campaign -- and that he condemned the shooting "in the strongest possible terms."

"I have just been informed that the alleged shooter at the Republican baseball practice is someone who apparently volunteered on my presidential campaign," Sanders said.

"I am sickened by this despicable act. Let me be as clear as I can be. Violence of any kind is unacceptable in our society and I condemn this action in the strongest possible terms," he said. "Real change can only come about through nonviolent action, and anything else runs against our most deeply held American values."

Capitol Hill increases security, cancels events

The news of the shooting reverberated on Capitol Hill, where security was increased and many regular proceedings were canceled or postponed.

In his remarks, Ryan also said he'd been moved by an image of members of the Democratic congressional baseball team huddled in prayer after learning of the shooting.

"Every day we come here to test and to challenge each other. We feel so deeply about the things that we fight for and the things that we believe in. At times, our emotions can clearly get the best of us. We are all imperfect. But we do not shed our humanity when we enter this chamber. For all the noise and all the fury, we are one family," Ryan said.

The House decided to not hold any votes on legislation Wednesday, and many hearings were delayed. The House Natural Resources Federal Lands Subcommittee also canceled a scheduled meeting to debate gun legislation

Capitol Hill Police notified congressional offices that the security presence on the Hill would be increased "out of an abundance of caution."

Members of Congress targeted in the past by violence

Scalise is the first member of Congress to be shot since former Arizona Rep. Gabby Giffords in January 2011. Giffords was shot in the head by Jared Lee Loughner at a "Congress On Your Corner" event outside a Tucson grocery store. Giffords, who authorities said was the main target of the shooting, survived the attack, but six others were killed and an additional 12 were injured.

Loughner pleaded guilty in 2012 and was sentenced to life in prison without the possibility of parole.

CORRECTION: An earlier version of this report misidentified this size of the a pistol recovered from the scene of the shooting. It was a 9 mm pistol. An earlier version of this story incorrectly described the SKS rifle.