Danielle Stella's campaign account tweeted: "If it is proved @ilhanMN passed sensitive info to Iran, she should be tried for #treason and hanged", according to The Washington Times.
The account later linked to a picture of a stick figure hanging from a gallows, the paper said,
On Thursday the account, @2020mncongress, had been suspended. A Twitter spokesperson told The Washington Times it had been permanently suspended.
In a statement Ms Stella said: "My suspension for advocating for the enforcement of federal code proves Twitter will always side with and fight to protect terrorists, traitors, pedophiles and rapists."
The comments that saw her account suspended appear to refer to reports picked up by right-wing media sites that Ms Omar, one of the first Muslim women to be elected to Congress, had passed sensitive information to Iran via Qatar.
The allegations were made in a court case by a Kuwaiti-born Canadian businessman.
Ms Omar, a member of the self-styled Squad of progressive Democrats in the House of Representatives, denied the accusation.
Her spokesperson told the Jerusalem Post: "Since the day she was elected, Saudi Arabian trolls and mouthpieces have targeted Omar with misinformation and conspiracy theories.
"The latest, outlandishly absurd story from a Saudi-funded media outlet is of course false and only the latest in that trend.
"The only people Representative Omar represents in Washington are the people of Minnesota's 5th District. She will continue to speak out against human rights violations around the world – whether it is war crimes in Yemen or the caging of children at our border – regardless of who commits them."
Ms Omar has become a favourite target of Donald Trump and his allies.
In July crowds at a Trump rally chanted "Send her back", following the president's suggestion that she and the three other – US-born – members of the Squad should "go home" to fix problems in other nations instead of criticising his policies in their own country.
Last week a man pleaded guilty to threatening to kill Ms Omar. Patrick Carlineo said someone should "put a bullet in her skull" because he had come to believe she was a supporter of Hamas and the Muslim Brotherhood, according to the US Attorney's office.
While he faces up to 10 years in prison and a $250,000 fine, Ms Omar wrote an open letter to the judge in the case asking him not to give a lengthy jail sentence or heavy fine.