Donald Trump fired a volley of insults at Senator Elizabeth Warren on Tuesday morning, 24 hours after she publicly released the results of a DNA test intended to prove her Native American ancestry.

Referring to her by the racist moniker Pocahontas, Trump said: “She took a bogus DNA test and it showed that she may be 1/1024 [Native American,] far less than the average American …

“Now that her claims of being of Indian heritage have turned out to be a scam and a lie, Elizabeth Warren should apologize for perpetrating this fraud against the American Public,” Trump continued.

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He was joined in criticism of Warren by the Cherokee Nation, who late on Monday released a statement about Warren’s disclosure. “Using a DNA test to lay claim to any connection to the Cherokee Nation or any tribal nation, even vaguely, is inappropriate and wrong,” said the Cherokee Nation secretary of state, Chuck Hoskin Jr.

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“It makes a mockery out of DNA tests and its legitimate uses while also dishonoring legitimate tribal governments and their citizens, whose ancestors are well documented and whose heritage is proven. Senator Warren is undermining tribal interests with her continued claims of tribal heritage.”

Trump gleefully incorporated the statement into his tweets at the Massachusetts senator, saying on Tuesday: “Now Cherokee Nation denies her, ‘DNA test is useless.’ Even they don’t want her. Phony!”

Warren’s DNA analysis was performed by a Stanford University professor, Carlos Bustamante, a highly respected researcher in the field of genetics. His findings, released in a campaign video from Warren’s 2018 Senate campaign that concluded Warren’s ancestry is mostly European but said “the results strongly support the existence of an unadmixed Native American ancestor”, six to 10 generations back. Trump’s reference to “1/1024” referred to the scenario that her native ancestor is 10 generations back.

The kerfuffle began during Warren’s 2012 Senate campaign when opponents accused her of having advanced her academic career as a law professor with the narrative that she is a descendant of Cherokee and Delaware tribes – using said claims to qualify for affirmative-action hiring considerations. In September 2017, a Globe investigation concluded that she did not.

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Still, Republicans generally, and Trump specifically, have seized on Warren’s claims of indigenous ancestry to paint her as a fraud and opportunist.

Warren was, at a few points during her academic career, described as minority faculty – at least once by her own election campaign on a forum. Warren has previously said that she checked a box to list herself as a minority in professional listings at her university from 1986 to 1995 in order to connect with “people like me”.

Warren has never claimed to be a member of a tribe, and made the distinction in her campaign video and again in a response to the Cherokee nation statement late on Monday. “I won’t sit quietly for [Trump’s] racism, so I took a test. But DNA & family history has nothing to do with tribal affiliation or citizenship, which is determined only – only – by Tribal Nations. I respect the distinction, & don’t list myself as Native in the Senate,” Warren said.

The senator also attempted to goad Trump into making good on a promise he had made to donate $1m to her favourite charity, “paid for by Trump, if you take the test and it shows you’re an Indian”. Warren asked him to cut a check to the National Indigenous Women’s Resource Center.

Trump said on Monday, while touring damage of Hurricane Michael in Florida, that the promise was contingent on her winning the 2020 Democratic primary and debating him during the campaign, and that he would only pay up if he could test her DNA “personally”.