A US senator mocked by Donald Trump over her ancestral claims has released the results of a DNA analysis that she said indicated she has some Native American heritage.

The move by Elizabeth Warren was a direct rebuttal to the president, who has long mocked her claims and repeatedly referred to her as Pocahontas.

The Democrat and potential 2020 presidential contender challenged Mr Trump to make good on his pledge to donate one million dollars to charity if she provided proof of Native American heritage, a moment that was caught on video.

Mr Trump falsely denied ever making the offer.

The analysis was done by Stanford University professor Carlos D Bustamante, a prominent expert in the field.

He concluded that the great majority of Ms Warren’s ancestry is European but added that the results “strongly support” the existence of a Native American ancestor.

In his report, Prof Bustamante said he analysed Ms Warren’s sample without knowing the identity of the donor.

He concluded that Ms Warren has a pure Native American ancestor who probably lived six to 10 generations ago, and that it was impossible to determine the individual’s tribal connection.

Ms Warren, who has said her Native American roots were part of “family lore”, also released a video produced by her Senate re-election campaign in Massachusetts.

In it, she said: “The president likes to call my mom a liar. What do the facts say?”

Prof Bustamante replied: “The facts suggest that you absolutely have Native American ancestry in your pedigree.”

The analysis is not the first evidence of Ms Warren’s heritage.

An 1894 document previously unearthed by the New England Genealogical Society suggested Ms Warren’s great-great-great-grandmother, O.C. Sarah Smith, was at least partially Native American, making the senator 1/32nd Native American.

The genealogy group has said it has no conclusive evidence of her ancestry, and a spokesman said it would not comment on the genetic findings.

However, if Ms Warren’s ancestor had been as much as 10 generations removed, it would make that individual a great-great-great-great-great-great-great-great grandparent, making her only 1/1,024th Native American, according to Blaine Bettinger, a genealogist and author who specialises in DNA evidence.

Such a finding could potentially further excite her critics instead of placating them.

Ms Warren’s effort to address questions about her ancestry and the release of the video are her latest moves telegraphing a likely presidential run in 2020.

During the summer she also released a decade worth of tax returns, drawing a contrast with Mr Trump’s unwillingness to release his own tax documents.

The moves seem to anticipate the type of criticism she might face against opponents in a Democratic primary or in a possible general election match-up against Mr Trump.

“She is most clearly doing the things you do if you’re running for president,” said Steve Elmendorf, a Democratic strategist and veteran of presidential campaigns.

During a recent town hall-style meeting in Holyoke, Massachusetts, Ms Warren said she planned to “take a hard look at running for president”, after next month’s election.

Earlier this year, the senator released personnel files seeking to dispute critics who have alleged that the former Harvard Law School professor advanced her law career with a narrative she is a descendant of Cherokee and Delaware tribes.

Ms Warren has denied using her Native American heritage to gain any advantage.

In an email on Monday to supporters, Ms Warren said she “never expected the president of the United States to use my family’s story as a racist political joke against Native American history, culture, and people – over, and over, and over”.

In a tweet directed at Mr Trump, Ms Warren said: “Remember saying on (July 5) that you’d give $1M to a charity of my choice if my DNA showed Native American ancestry?”

She went on to request that the president send a cheque to the National Indigenous Women’s Resource Centre.

At a summer rally in Montana, the president declared that he would give a million dollars to charity, “paid for by Trump”, if Ms Warren takes the test “and it shows you’re an Indian”.

But when asked by reporters on Monday, Mr Trump said: “I didn’t say that.”

Ms Warren, who grew up in Norman, Oklahoma, said her mother and father were forced to elope because of her mother’s heritage.

She faces Republican Geoff Diehl, who co-chaired Mr Trump’s Massachusetts presidential campaign, in the November 6 election.

The DNA analysis was first reported by The Boston Globe.