A Republican congressman has spread false allegations that the US representative Ilhan Omar denied the September 11 hijackers were terrorists, as part of a new wave of abuse directed at her by some conservatives.

Representative Dan Crenshaw of Texas shared a tweet falsely reporting that Omar had said she “does not consider [September 11] a terrorist attack on the USA by terrorists”, while accusing the Minnesota congresswoman of playing down the attack.

Crenshaw was responding to a short video clip of a speech given by Omar in California last month, when she complained that all Muslims suffered the consequences of the actions by a small group of them on 11 September 2001, when al-Qaida terrorists hijacked four passenger jets and flew them into the World Trade Center in New York and the Pentagon building outside Washington, while one crashed in a field in Pennsylvania.

Crenshaw was joined by Ronna McDaniel, the Republican party chairwoman, who claimed Omar had shown she was “anti-American”, and the Fox News host Brian Kilmeade, who questioned Omar’s loyalty to the US during a broadcast on Wednesday morning.

Omar described the attacks against her as “dangerous incitement” and urged colleagues to condemn them. She said: “My love and commitment to our country and that of my colleagues should never be in question. We are ALL Americans!”

Last week, a supporter of Donald Trump in upstate New York was charged with threatening to kill Omar, one of the first Muslim women to serve in the US Congress. Patrick Carlineo was arrested after telephoning Omar’s office and stating that he would shoot her. Carlineo told the FBI “that he was a patriot, that he loves the President, and that he hates radical Muslims in our government”, according to a criminal complaint.

The latest round of attacks on Omar by Republicans was prompted by the publication on Tuesday of a snippet from a speech she gave last month to an event hosted by the Council on American-Islamic Relations (Cair), in which she referred to the September 11 attacks.

“Cair was founded after 9/11 because they recognised that some people did something, and that all of us were starting to lose access to our civil liberties,” Omar said. The remark was criticised by Crenshaw and others, who said Omar’s description minimised September 11 and its perpetrators.

But a video of Omar’s full speech shows that the disputed remark followed from comments only a minute earlier in which Omar did mention terrorism. She complained that Islam was discussed in schools only in relation to Muslim terrorists.

“It doesn’t matter how good you are if you, one day, find yourself in a school where other religions are talked about, but when Islam is mentioned, we are only talking about terrorists, and if you say something, you are sent to the principal’s office,” she said.

A spokeswoman for Crenshaw, a retired navy Seal, did not respond to a request for comment.

Despite the allegations from McDaniel and Fox News, Omar also used the speech to praise the US as “a country that was founded on religious liberty”. Omar arrived in the US during the 1990s as a child with her family, who were refugees from Somalia.

“I know as an American, as an American member of Congress, I have to make sure that I am living up to the ideals of fighting for liberty and justice. Those are very much rooted in the reason why my family came here,” she said in the speech.