In the face of attacks from Donald Trump, Republicans and rightwing media outlets, the Minnesota representative Ilhan Omar said on Saturday no one could “threaten” her “unwavering love for America”.

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“I did not run for Congress to be silent,” Omar wrote on Twitter, less than a day after the president shared a video that included footage of her speaking and graphic images of the 9/11 terror attacks. Trump retweeted his message on Saturday.

Omar thanked supporters for standing “against an administration that ran on banning Muslims from this country”.

“No one person – no matter how corrupt, inept, or vicious – can threaten my unwavering love for America,” she wrote on Twitter. “I stand undeterred to continue fighting for equal opportunity in our pursuit of happiness for all Americans.”

In the hours after the president attacked Omar, who came to the US from Somalia as a refugee and became one of the first Muslim women in Congress, progressive Democrats condemned the president for “inciting violence” against her. Just last week, a Trump supporter from New York state was charged with threatening to kill Omar.

But while presidential candidates rallied behind Omar, House leaders did not immediately take the same approach.

The president is inciting violence against a congresswoman Elizabeth Warren

Leadership and some freshmen Democrats have disagreed over how to respond to attacks on Omar, including accusations that her criticism of US policy on Israel was antisemitic. Last month, Omar apologized “unequivocally” after suggesting support for Israel was fueled by donations from a lobby group.

On Saturday morning, Speaker Nancy Pelosi hedged her response to Trump’s tweet, saying “the president shouldn’t use the painful images of 9/11 for a political attack” but not mentioning Omar.

“The memory of 9/11 is sacred ground, and any discussion of it must be done with reverence,” Pelosi wrote, a comment that could be read as a criticism of Omar as well as the president. “It is wrong for the president, as commander-in-chief, to fan the flames to make anyone less safe.”

Trump tweeted “WE WILL NEVER FORGET!” with a video edited to suggest Omar was dismissive of the attacks. The video used part of a speech last month to the Council on American-Islamic Relations in which Omar discussed the problem of Islamophobia, describing “the discomfort of being a second-class citizen”. After September 11, she said, advocates “recognized that some people did something, and that all of us were starting to lose access to our civil liberties”.

Rightwing politicians were quick to say Omar was dismissing the gravity of 9/11. Dan Crenshaw, a congressman from Texas who as a Navy Seal was seriously injured in Afghanistan, falsely claimed Omar “does not consider [September 11] a terrorist attack on the USA by terrorists”.

Two of the most progressive candidates for the Democratic nomination called on all lawmakers to condemn such attacks. Senator Bernie Sanders called attacks on Omar “disgusting and dangerous” and said Omar would not “back down to Trump’s racism and hate, and neither will we”.

Senator Elizabeth Warren said: “The president is inciting violence against a sitting congresswoman – and an entire group of Americans based on their religion. It’s disgusting. It’s shameful. And any elected leader who refuses to condemn it shares responsibility for it.”

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Pete Buttigieg, the mayor of South Bend, Indiana who has surged in 2020 polls, wrote: “After 9/11 we all said we were changed. That we were stronger and more united. That’s what ‘never forget’ was about. Now, a president uses that dark day to incite his base against a member of Congress, as if for sport. As if we learned nothing that day about the workings of hate.”

Buttigieg added: “The threats against the life of [Omar] make clear what is at stake.”

Among other candidates, former Hud secretary Julián Castro said he stood with Omar and “others targeted by the president’s anti-Muslim rhetoric”. Former congressman Beto O’Rourke said: “We are stronger than this president’s hatred and Islamophobia. Do not let him drive us apart or make us afraid.”

The California senator Kamala Harris wrote: “For two years, this president has used the most powerful platform in the world to sow hate [and] division. Putting the safety of a sitting member of Congress at risk [and] vilifying a whole religion is beyond the pale. I’ll be blunt – we must defeat him.”

Facebook Twitter Pinterest Ilhan Omar, with Democratic representative Sheila Jackson Lee and Nancy Pelosi outside the Capitol. Photograph: J Scott Applewhite/AP

Fox News and the New York Post, owned by Rupert Murdoch, have devoted high-profile coverage to misleading claims about Omar’s words. Republican party chair Ronna McDaniel has also attacked the congresswoman. Rashida Tlaib, the other Muslim American woman in Congress, was the first on Friday to call for Democrats to “speak up” in return.

“Enough is enough,” she wrote. “No more silence, with NY Post and now Trump taking Ilhan’s words out of context to incite violence toward her, it’s time for more Dems to speak up. Clearly the GOP is fine with this shameful stunt, but we cannot stand by.”

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Trump’s own comments and falsehoods about September 11 have long attracted criticism.

He has repeated false claims about “thousands and thousands of” Muslims in New Jersey celebrating on the day itself; his business received money meant for small businesses affected by the attack, even though his businesses were not; he has claimed to have helped clear rubble from the attack site, a claim for which evidence does not exist; he has said he watched people jump from the World Trade Center towers from Trump Tower, four miles away, which would not be possible.

Perhaps most famously, in an interview hours after the attack on the World Trade Center, part of attacks in which 2,977 people were killed, Trump described his shock and disbelief. Then he added a comment that left his interviewers “stunned”.

Trump, claimed, falsely, that one of his own buildings had been “the second-tallest building in downtown Manhattan”, after the World Trade Center.

“And now it’s the tallest,” he said.