The tribe's secretary of state, Chuck Hoskin Jr., said using a DNA test to suggest ties to the Cherokees or any tribal nation, "even vaguely, is inappropriate and wrong".
Warren released test results of a DNA analysis earlier this week that showed she had a distant Native American ancestry.
The President's latest triumph in this regard is the revelation of the results of Senator Elizabeth "Fauxcahontas" Warren's DNA test. "Let them have their story".
"Your viewers need to understand how deceptive Elizabeth Warren was".
Both Harvard and the University of Pennsylvania listed her as "Native American" on their federal labor forms. Ms. Warren first denied listing herself as a "minority professor", or ever saying that she was Cherokee.
Warren has in the past claimed to be part Cherokee, a claim that has led to criticism that she played up a thin claim to minority status in order to advance her academic career.
"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".
Readers will know the background already: Elizabeth Warren claimed to be Native American while she was a law professor at Harvard despite (a) appearing about as Anglo-white as one can appear and (b) having scant evidence that her claim of Native American heritage was true.
Monday night Warren tweeted, "At the end of the day, I trust the people of MA to look at the facts about who I am and how I've lived my life and make their own judgment about me".
Trump simply doubled down attacks he'd been making for years, simultaneously belittling Warren and Native Americans.
One 2014 study found that, on average, European Americans tested for 0.18 per cent Native American ancestry. Warren had issued a modest disclaimer in saying that, "DNA & family history has nothing to do with tribal affiliation or citizenship, which is determined only - only - by Tribal Nations".
Trump gleefully incorporated the statement into his tweets at the MA senator, saying on Tuesday: "Now Cherokee Nation denies her, 'DNA test is useless.' Even they don't want her. Phony!"
After playing the video of Trump's promise, Goldberg opened the discussion by asking if the president "owes her some money".
"If you're like most people, a sliver of Native American coding in your DNA is no more than a colorful bit of family trivia", the Globe wrote.
As well as giving Trump an opening to keep the story going on his terms just three weeks from make-or-break mid-term elections, "liberals generally should regard this whole thing as a cautionary tale", says Ros Douthat in The New York Times.
"He's trying to do what he always does to women who scare him: call us names, attack us personally, shrink us down to feel better about himself", Warren said on Twitter. She is also reinforcing one of the most insidious ways in which Americans talk about race: "as though it were a measurable biological category, one that, in some cases, can be determined by a single drop of blood". "Harvard called her "a person of color" (amazing con), and would not have taken her otherwise!"
However the announcement has provoked the ire of the Cherokee Nation, headquartered in Oklahoma, which has accused Ms Warren of "undermining tribal interests with her continued claims of tribal heritage".