US senator Elizabeth Warren has suggested President Donald Trump’s comment about personally administering a DNA test to her to prove her Native American heritage is “creepy”.

She tweeted that the president makes “creepy physical threats” about women who scare him, including her.

The Massachusetts Democrat wrote: “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.

“It may soothe his ego – but it won’t work.”

Ms Warren, who is seen as a potential 2020 challenger to Mr Trump, appears to have followed the president’s tactics, striking back almost instantly at the president who continues to ridicule her claim of Native American ancestry.

Mr Trump relishes a good fight, those close to him have said, and will hit back twice as hard when he has been attacked.

A sharp critic of Mr Trump, Ms Warren wasted little time going after him following his comments during an appearance in Georgia.

She opened the day by releasing DNA test results that provide some evidence of a Native American in her lineage, though the ancestor probably lived six to 10 generations ago, according to the analysis.

Mr Trump has ridiculed her as “Pocahontas” over the ancestry claim.

In July, the president offered to donate one million dollars to her favourite charity if a DNA test proved her Native American bloodline.

On Monday, he denied ever making such a promise, then said later: “I’ll only do it if I can test her personally.

“That will not be something I enjoy doing either,” he added.

Donald Trump
Mr Trump has mocked Ms Warren, a possible contender to take him on in the 2020 elections (AP)

Ms Warren tweeted that Mr Trump is a “cowardly elitist” and she “won’t sit quietly for Trump’s racism”, so she took the test.

“I took this test and released the results for anyone who cares to see because I’ve got nothing to hide. What are YOU hiding, @realDonaldTrump?” she wrote.

“Release your tax returns – or the Democratic-led House will do it for you soon enough. Tick-tock, Mr President.”

Ms Warren was referring to the November 6 election, when Democrats hope to regain control of the US House of Representatives, which would put them in a position to examine and possibly publicly release Mr Trump’s tax returns.

Mr Trump has bucked decades of precedent by refusing to release his income tax returns during the 2016 presidential election, and continued with this stance after taking office.

Mr Trump on Tuesday hit back at Ms Warren in a tweet.

The president wrote: “Pocahontas (the bad version), sometimes referred to as Elizabeth Warren, is getting slammed. She took a bogus DNA test and it showed that she may be 1/1024, far less than the average American. Now Cherokee Nation denies her, “DNA test is useless.” Even they don’t want her. Phony!”