Ms Greene, continuing with the confrontation on Twitter, wrote on Thursday that Ms Ocasio-Cortez was a “fraud and a hypocrite” who was calling for further Capitol security despite being “Ms Defund The Police”.
It followed two reporters from The Washington Post witnessing Ms Greene accosting the Democrat on Wednesday.
Ms Ocasio-Cortez, who was apparently walking away and was refusing to acknowledge repeated screams of “Hey Alexandria!,” eventually threw her hands up in “exasperation” at Ms Greene.
“You don’t care about the American people,” Ms Greene allegedly screamed, falsely referring to activists and Black Lives Matter organisations as “terrorists”. “Why do you support terrorists and antifa?”
The GOP congresswomen allegedly went on to call the Democrat a “chicken” and a “coward” for refusing to argue with her, in front of reporters inside the Capitol on Wednesday evening.
In a statement, Ms Ocasio-Cortez’s office told the Post that “We hope leadership and the Sergeant at Arms will take real steps to make Congress a safe, civil place for all Members and staff”.
On Thursday, Ms Greene continued by saying that the Democrat “[lacked] the courage & intelligence to debate”, and false accused Ms Ocasio-Cortez of supporting Hamas, a Palestinian terrorist group currently in confrontation with Israeli forces.
Following the Post’s report, Twitter users called for Ms Greene’s arrest, or for Ms Greene to be completely removed from the chamber.
“Why is MTG allowed to get away with this behaviour?,” asked Cateyes, a Twitter user. “This is not acceptable in the Republican or Democrat Senate and Congress. In fact this isn’t acceptable in public, she’s a bully!”
“AOC also should get a restraining order against MTG. She has to be shut down even arrested if necessary. Folks have to stop giving her a pass to abuse others with her insanity,” wrote Dr Vicki Ross-Norris.
“MTG is a bully,” added Laura Baker, “and, the GOP ousts a well spoken, intelligent Republican in Cheney. I don’t get it. McCarthy is policing the wrong people.”
The confrontation followed the ouster of Liz Cheney as Republican conference chair on Wednesday, after calls from Trump-supporting members of the GOP, including Ms Greene and House minority leader Kevin McCarthy.
Following the Capitol insurrection in January, Ms Ocasio-Cortez told CNN that she still worries about her safety among Trump allies in the GOP repeatedly downplaying the insurrection.
Ms Greene told reporters on Wednesday of Ms Ocasio-Cortez: “She’s a chicken, she doesn’t want to debate the Green New Deal. These members are cowards. They need to defend their legislation to the people. That’s pathetic.”