"This is something that should have never happened," Armando Florido, one of the members, said on "Fox & Friends" on Friday.
"This is something that should have been taken care of on his first offense while he was trying to become a citizen of this country, this great country that we live in."
The Thin Blue Line is comprised of retired or current members of law enforcement.
"It's a simple fact that this guy should have been one or two places. He should have either been in jail or he shouldn't have been in our country at the time," added Rico Garcia, another member.
Ivan Robles Navejas, 28, a Mexican native, was arrested for allegedly crashing into members of the club while driving under the influence. Law enforcement officials said he crossed the center stripe on Highway 16 south of Kerrville before slamming head on into the motorcyclists.
Navejas has a long criminal history, including convictions for resisting arrest and a DUI. He faces multiple counts of intoxicated assault with a vehicle and intoxicated manslaughter with a vehicle.
Three members of the club were killed in the crash. They were identified as Joseph Paglia, Jerry Wayne Harbour, and Michael White.
"These men who spent their lives serving our country and their communities with valor and honor," Thin Blue Line said in a statement to news outlets.
The group on its website asked people to pray for the families of the men, as well as members who were left injured by "this senseless and tragic accident."
According to the Kerr County Sheriff's Office, four members were rushed to the hospital in critical condition after the crash.
Immigration and Customs Enforcement (ICE) confirmed this week that Navejas is an illegal immigrant from Mexico.
The law enforcement agency filed an immigration detainer, seeking to keep him locked up even if local officials move to release him.
Immigration officers encountered Navejas after a driving while intoxicated arrest in Kerr County in November 2016 but he didn't meet ICE's priorities at the time, a spokeswoman said, a reference to the Obama administration's de-emphasis on deportations in the later years of his second term.
Navejas was shielded from deportation from 2013 to 2015 through the Deferred Action for Child Arrivals program, which was implemented by former President Barack Obama through executive order. He was a conditional permanent resident but that status expired in January 2019.
Garcia, the club member, said on Fox that the crash reminded him of when an illegal immigrant caused a fatal crash last year that left seven motorcyclists dead.