Later on Friday, Omar sent a tweet calling for House leadership to take "appropriate action."
Omar added that "normalizing this bigotry not only endangers my life but the lives of all Muslims."
In an undated video that went viral on Thursday, Boebert said that she was getting into an elevator with one of her staffers when a Capitol police officer rushed over to the elevator with "fret [sic] all over his face," trying to open the door as it was closing.
She then claimed that, upon seeing Omar to her left, she said: "Well, she doesn't have a backpack. We should be fine," implying that Omar could have been carrying explosives in a backpack -- an anti-Muslim trope.
Boebert also called Omar a part of a so-called "jihad squad" twice in the video.
"I apologize to anyone in the Muslim community I offended with my comment about Rep. Omar. I have reached out to her office to speak with her directly. There are plenty of policy differences to focus on without this unnecessary distraction," Boebert tweeted on Friday.
I apologize to anyone in the Muslim community I offended with my comment about Rep. Omar. I have reached out to her office to speak with her directly. There are plenty of policy differences to focus on without this unnecessary distraction.— Rep. Lauren Boebert (@RepBoebert) November 26, 2021
Omar said on Thursday that Boebert made up the story, and said that anti-Muslim racism should not be allowed in Congress.
"Fact, this buffoon looks down when she sees me at the Capitol, this whole story is made up," Omar tweeted on Thursday night. "Anti-Muslim bigotry isn't funny & shouldn't be normalized. Congress can't be a place where hateful and dangerous Muslims tropes get no condemnation."
Omar received support from some fellow representatives, including Rep. Ayanna Pressley (D-Mass.), who called Boebert's remarks "shameful, deeply offensive and dangerous."
Rep. Rashida Tlaib (D-Michigan), another Muslim member of Congress, wrote on Thursday night, "These pathetic racist lies will not only endanger the life of @IlhanMN, but will increase hate crimes towards Muslims. The continued silence & inaction towards this hate-filled colleague and others is enabling violence. It must stop."
One representative across the aisle, Rep. Adam Kinzinger (R-Illinois), retweeted the video with the comment, "Boebert is TRASH." Republican congressional leaders have not commented yet on Boebert's remarks.
Edward Mitchell, deputy director of the Council on American-Islamic Relations, told CNN on Friday morning that Boebert's comments were "beyond the pale."
"You've gotta remember, Lauren Boebert is not some comedian at a club. She is a sitting member of Congress speaking to her constituents... I will say the more disturbing thing is that the audience applauded, and laughed, and that Republican leaders did not condemn this yet," Mitchell said.
ABC News' Lauren Minore contributed to this report.
The video in the media player above was used in a previous report.