Barth, a 24-year-old legislative correspondent in Williams' office, is from the Houston-area.
Officers Crystal Griner and David Bailey were among the five injured after a gunman opened fire on congressmen during the practice.
Williams arrived at a news conference in Washington using crutches and said he would be returning to Texas later this week for further treatment.
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Wu Xiaohui , the chairman of Anbang Insurance, was "unable to perform his duties for personal reasons", the company said. Wu previously established Liantong Leasing Group in 1996 and Traveller Automobile Group in 1998, before joining Anbang.
- Rep. Roger Williams (@RepRWilliams) June 14, 2017We ask that you please respect the privacy of him and his family during this hard time.
In an interview on the situation, Rep. Williams said Barth never stopped texting his colleagues to share updates and information on the situation, even after he was hit and bleeding. Rep. Williams has been the coach of the team since he joined Congress in 2013.
In a tweet, Tim Walz said "My prayers go out to the victims of the congressional baseball practice shooting".
"I don't think it was a Republican or Democratic issue, but I think he had an issue", Williams said. "I held him and he held me", Williams said. "The thin blue line held today and America should be thankful that this is still the type of country that produces these types of heroes. Some of us were on the ground", Barton said.
"I just want to thank the security detail because they saved our lives", Barton said.
Williams said he dove into the concrete floor of the first-base dugout, which he described as being "like diving into a swimming pool without water". "Jeff Flake took his belt off and made a tourniquet around Zack's leg to stop the bleeding". Alexandria police say the suspect is in custody.