"Congresswoman Omar is quick to describe all criticism of her as racism," Carlson said Wednesday on "Tucker Carlson Tonight."
"She has done that quite a bit, but in fact, there are serious reasons to wonder about her judgment and her competence. The evidence suggests that she is an extremist on virtually every topic and has been for quite some time."
Carlson pointed to video showing Omar appearing concerned that a professor she once had in college gesticulates differently when he mentioned the terror group Al Qaeda.
In the clip, Omar recalled taking a class on terrorism.
"Every time the professor said 'Al Qaeda,' he sort of like, his shoulder sort of went up -- 'Al Qaeda.'," she said.
"And you don't say 'America' with an intensity. You don't say 'England' with intensity. You don't say 'the Army' with an intensity."
The evidence suggests that she is an extremist on virtually every topic and has been for quite some time
Additionally, Carlson recalled how Omar was criticized for seemingly referring to the 9/11 terror attacks by saying, "some people did something."
He also pointed to a 2017 tweet from Omar criticizing U.S. military forces and claiming they killed "thousands" during an operation in Mogadishu, Somalia that later became the basis for the 2001 film, "Black Hawk Down."
"In his selective memory, he forgets to also mention the thousands of Somalis killed by the American forces that day!" Omar tweeted in response to another Twitter user who wrote that 19 service members were killed in the "worst terror attack in Somalia" during the "Battle of Mogadishu."
In his remarks, Carlson said Americans were "attacked while trying to protect her homeland from warlords." Omar was born in Somalia.
The host also condemned remarks Omar made criticizing Christianity and "religious fundamentalists."
"Religious fundamentalists are currently trying to manipulate state laws in order to impose their beliefs on an entire society," she said. "All with complete disregard for voices and the rights of American women."
Carlson said the remarks he replayed -- as well as those calling for abolishing ICE and the need to "fight back against the criminalization of immigrants," depict Omar as "someone clearly with a long history of irresponsible and unsupportable statements."
"In some cases, lunatic statements. But it's not just what she says, it's what she does. Omar's past is also full of legal and ethical lapses."
"Keep in mind... this is not just a member of Congress, this is a hero -- this is a living folk hero on the left. This is someone lionized every day, by, for example, CNN."
Fox News' Joseph Wulfsohn contributed to this report.