"Hell, yes, we're going to take your AR-15", Mr O'Rourke, a former Democratic Texas congressman, said on the debate stage in Houston.
Fox News quoted an exchange between O'Rourke's and Hasty that began with the host saying, "I own an AR-15".
Meanwhile, a Texas state lawmaker sent a threatening tweet, which O'Rourke reposted with the message, "Clearly, you shouldn't own an AR-15-and neither should anyone else".
Cain shot back: "You're a child Robert Francis".
Thousands responded to the tweet before it was taken down, and Cain engaged with some.
The U.S. Secret Service said Friday that O'Rourke is not now under the agency's protection and declined to comment further.
At Thursday night's Democratic presidential debate, O'Rourke was pressed by ABC's "World News Tonight" anchor David Muir about whether he was proposing "taking away" guns from lawful gun owners. "You're an idiot", he told one commenter.
O'Rourke emphasized Friday morning that his buy-back plan was "not voluntary". "Any time you have somebody threaten to use violence against somebody in this country to resolve a political issue, or really for any reason, that's a matter for law enforcement", O'Rourke said in an interview on CNN on Friday.
His tweet came during a politically charged moment in Texas over gun control following the El Paso shooting and a Labor Day weekend rampage in West Texas that left seven people dead. AR stands for Armalite rifle. In that massacre, a white gunman targeting Hispanic people used an AK-47 to fatally shoot 22 people in an El Paso Walmart. He's long supported buybacks of such weapons.
O'Rourke has made addressing gun violence and mass shootings a central theme of his presidential campaign over the last few weeks after a series of mass shootings, including one in his hometown of El Paso, rocked the U.S.in August. "People were murdered. The language you are using and the way you are using it is unsafe".
The O'Rourke campaign reported the tweet to the Federal Bureau of Investigation, a campaign spokesperson told the Guardian. "I think it's a really irresponsible thing for him to do", he added, "especially somebody who is a public servant and in a position of public trust to be sending that kind of message".
Cain is a lawyer who was first elected in 2016 and is part of the small Freedom Caucus in the Texas House that represents the GOP's most socially conservative wing. Typically, the publication explained, freshmen lawmakers are exempted from the list, but they cited Cain's "uninformed and belligerent performance".
In 2018, police were called to remove Mr Cain from the state Democratic convention after he showed up with a pistol and pro-gun pamphlets, the Fort Worth Star-Telegram reported.