Donald TrumpDonald John TrumpThe Hill's Morning Report - White House, Congress: Urgency of now around budget GOP presses Trump to make a deal on spending Democrats wary of handing Trump a win on infrastructure MORE is sticking with his moniker of Sen. Elizabeth WarrenElizabeth Ann WarrenThe Memo: Trump faces steep climb to reelection Feehery: A whole new season of 'Game of Thrones' Overnight Energy: Warren wants Dems to hold climate-focused debate | Klobuchar joins candidates rejecting fossil fuel money | 2020 contender Bennet offers climate plan MORE (D-Mass.) as "Pocahontas" after being challenged at a news conference by an attendee who called it offensive.

Trump responded in a tweet on Thursday afternoon, saying that it was "offensive" that Warren "pretended to be Native American to get in Harvard."

Warren fact-checked Trump in a pair of tweets herself:

The exchange came after a person in the audience for a news conference earlier in the day in Bismarck, N.D., challenged Trump on his moniker for Warren.

"Who, Pocahontas?" Trump responded when asked about Warren.

"Is that offensive?" someone asked.

"Is it offensive? You tell me," Trump said.

"That's very offensive!" yelled out a woman from the audience, who was later identified as Nicole Robertson, a freelance writer credentialed for the event. She is a member of the Cree nation.

"Oh yeah, I'm sorry about that," Trump said sarcastically, before repeating the name. "Pocahontas? Is that what you said? Elizabeth Warren?"

Trump has used the moniker several times in going after Warren's old claims of Native American ancestry. On Thursday he also called her "overrated" and "a real disaster."

"She said she was a Native American, but she wasn't able to document it," Trump said, mocking Warren for talking about her "high cheek bones" to explain her ancestry. "I think she's as Native American as I am."