Asked by a reporter at a New York event on Monday if she would apologise for saying he almost had her “murdered”, Ms Ocasio-Cortez said "That’s not the quote and I will not apologise for what I said," in a video captured byThe New York Post.
Before Ms Ocasio-Cortez could complete her response the interview was cut off by a companion saying, "I think we're actually done this morning".
The Independent has reached out to Ms Ocasio-Cortez's office for comment.
House Republicans have called on House Speaker Nancy Pelosi to make Ms Ocasio-Cortez apologise and retract the comments accusing Mr Cruz of “attempted murder”.
"It is completely unacceptable behaviour for a member of Congress to make this kind of scurrilous charge against another member in the House or Senate for simply engaging in speech and debate regarding electors as they interpreted the Constitution,” Texas Republican Chip Roy wrote in a letter to Ms Pelosi.
Ms Ocasio-Cortez's comment was made in response to a quote tweet from Mr Cruz saying he "fully agreed" with the Democratic Congresswoman's criticism of the Robinhood app suspending trading at the height of the GameStop frenzy just over a week ago.
"I am happy to work with Republicans on this issue where there’s common ground, but you almost had me murdered 3 weeks ago so you can sit this one out," Ms Ocasio-Cortez began.
"Happy to work w/ almost any other GOP that aren’t trying to get me killed. In the meantime if you want to help, you can resign."
In the Twitter thread, Ms Ocasio-Cortez said Mr Cruz "had a role" in the attacks that lead to five people, including a Capitol police officer, losing their lives.
"This isn’t a joke. We need accountability, and that includes a new Senator from Texas," she said.
"In the meantime, you can get off my timeline & stop clout-chasing. Thanks. Happy to work with other GOP on this."
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