Ms Greene, a controversial GOP members of Congress, was overheard accosting Ms Ocasio-Cortez on Wednesday evening by two reporters from The Washington Post .
Ms Green ran towards the Democrat, who was apparently walking away from her and refusing to acknowledge repeated screams of “Hey Alexandria!”
“You don’t care about the American people,” Ms Greene screamed, falsely referring to activists and Black Lives Matter organisations as “terrorists”. “Why do you support terrorists and antifa?”
The reporters from the Post then witnessed Ms Ocasio-Cortez throwing her hands up in the air in “exasperation” at Ms Greene’s antics.
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”.
“Especially as many offices are discussing reopening. One Member has already been forced to relocate her office due to Congresswoman Greene’s attacks,” Ms Ocasio-Cortez’s statement added, referring to Rep Cori Bush.
Following the report, Twitter users called for Ms Greene’s arrest, or for the Republican 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.”