Host Brian Kilmeade called Ocasio-Cortez's argument about implementing universal background checks "fact-challenged" after she criticized people who share guns in other parts of the country.
The U.S. representatives' war of words began when Crenshaw tweeted about a Houston-area woman who used a handgun to defend herself when five men tried to rob her.
“Situations like this story are why we protect the 2nd Amendment,’ Crenshaw tweeted.
He added: “Side note: With universal background checks, I wouldn’t be able to let my friends borrow my handgun when they travel alone like this. We would make felons out of people just for defending themselves.”
Ocasio-Cortez quickly replied, asking why he is “lending” people his guns and accusing the Texas lawmaker of giving firearms to people who have “likely abused their spouse or have a violent criminal record.”
Crenshaw then questioned why Ocasio-Cortez thinks his friends are domestic abusers and criminals, and argued that people loan one another guns for self-defense and hunting.
Crenshaw then took a shot at Ocasio-Cortez’s hometown, saying, “This is America outside NYC.” Ocasio-Cortez responded by noting that New York "is one of the safest states in the country when it comes to guns, incl rural areas."
"Try to keep up," she wrote.
Host Ainsley Earhardt said she grew up in South Carolina, where hunting is common, and people share guns and loan each other guns routinely.
"It doesn't mean that they're abusing their spouse at home, or are violent or have criminal records. AOC can say that, she lives in New York City, that's fine, she can have her opinion. But she's not educated when it comes to what people are using their guns for in other parts of the country," said Earhardt.
Kilmeade said Congress is set to debate the private sales of firearms that occur without background checks.
"You can have a healthy, good discussion, hear both sides. You don't have to accuse someone of abusing their wife if they borrow someone's gun," said Earhardt.
On "The Ingraham Angle" Wednesday, gun rights advocate Colion Noir said many gun control supporters on the left speak from an "emotional place" about firearms due to a lack of knowledge or experience on the issue.
"The only thing they can go to is emotion," said Noir.
Fox News' Andrew O'Reilly contributed to this report.