He added the shooter was "taken down". The official was not authorized to discuss an investigation by name and spoke on condition of anonymity.
The Associated Press is reporting that a government official says the suspect has been identified as an IL man named James.
In a live statement after the incident, Trump said that Hodgkingson had died from his injuries and praised the "heroic" actions of Capitol Police officers. Steve is one of the finest men and most dedicated public servants I have ever known, and I expect his faith and strength of character will carry him through this ordeal.
Capitol police said it had increased police presence at the Capitol on Wednesday morning out of "an abundance of caution", as Republican politicians gave vivid descriptions of the shooting.
A Capitol Hill aide and two police officers were also wounded in the shooting.
White House spokesman Sean Spicer earlier said the President and the Vice President were aware of the situation. An ATF spokeswoman said a trace of the weapons would answer that question.
The incident injured five people injured, including House Majority Whip Steve Scalise.
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Five minutes in, Livermore struck a post after seeing his shot deflected, and the resulting melee was eventually cleared for a corner.
The FBI is investigating a shooting at a baseball field in Alexandria, Virginia, that injured at least four people, including a congressman.
Republican Senator Jeff Flake said Mr Scalise was shot in the left hip. House Majority Whip Steve Scalise was shot in the hip, and his office says he is undergoing surgery at MedStar Washington Hospital Center. Williams, who has coached the Republican baseball team since 2013, was not shot, despite reports in some media outlets.
The two Capitol police officers that were shot are in "good condition" and are being treated at a hospital, Capitol Police Chief Matthew Verderosa said.
Trump offers his own prayers to the Scalise family, and says the entire world is also praying for them.
"We are deeply saddened by this tragedy", he said.
Rep. Davis (R-Ill) said he and other Congress members ran and took for cover when shots were fired.
Scalise and several other GOP leaders and staff fembers were practicing for a bipartisan Congressional baseball game scheduled for Thursday evening.
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