WASHINGTON — It is a racial taunt made by the president of the United States, not unlike his discredited claim that Barack Obama was not born in America.

And just as President Trump’s embrace of birtherism led to the remarkable spectacle of President Obama’s birth certificate being distributed in the White House, Mr. Trump’s unrelenting mockery of Senator Elizabeth Warren as “Pocahontas” — questioning her claims about having Native American heritage — has prompted Ms. Warren to release the results of a DNA test that she says provide proof of her ancestry.

There is “strong evidence” that Ms. Warren has Native American pedigree “6-10 generations ago,” according to a document she released Monday from Dr. Carlos Bustamante, a renowned geneticist. The error rate is less than one-in-a-thousand, he said.

Ms. Warren’s elaborate attempt to neutralize Mr. Trump’s attacks represented the surest sign yet that she intends to run for president in 2020. Not only did the Massachusetts senator release the DNA results, but she created a fact-check website that details her Native American ancestry and her Oklahoma roots. The site also includes documents that Ms. Warren says make clear her heritage “had no role whatsoever” in her advancement during her academic rise as a Harvard law professor — as some Republicans have asserted.