U.S. Sen. Elizabeth Warren won’t be handing over a DNA test to President Donald Trump anytime soon.

In a wide-ranging interview Monday on Greater Boston, the Massachusetts Democrat offered a rebuttal to the president who, at a rally last week, invoked his controversial nickname for her, issued a hypothetical challenge to her heritage and mocked the Me Too movement.

But when asked whether she believed Trump was either racist or misogynistic for making those comments, she repeatedly referred to him as a “bully.”

“Oh, come on. He’s principally a bully and he’ll use anything that he thinks is going to make him big and tough and manly and roll over everybody else. I know what he’s trying to do, he’s trying to bully me and he’s trying to bully women all across this country,” Warren told Jim Braude.

Last week in Montana, Trump told supporters that if he got to debate Warren, he would challenge her to take DNA test in exchange for donating $1 million to her favorite charity but would “gently” toss the kit to her because “we’re in the Me Too generation.”

“Why not just give into a bully and get it off the table? Because it’s not how you deal,” she said, responding to a question about why she wouldn’t simply take the test, potentially neutralizing a politically potent issue.

Warren’s claims of Native American heritage have dogged her since the start of her political career. Trump often mocks and taunts her with the moniker “Pocahontas,” which some perceive as a racial slur.

Warren, widely spoken of as a potential 2020 challenger to Trump, is in the middle of her re-election campaign. Republicans state Rep. Geoff Diehl, Beth Lindstrom and John Kingston, and an independent Shiva Ayyadurai are all vying to take her on in November.

Asked to respond to criticism that she also engages in harsh rhetoric, Warren resisted.

“Well, first of all, I don’t think I’ve gone low. I’ve called out a bully for bullying. I haven’t called him names. I haven’t made jokes about size of anything. I haven’t — that hasn’t been the way I’ve gone after it,” she said.

Warren says she tries to keep her criticism of Trump focused on issues he “doesn’t want to talk about” — counting health care, infrastructure, and the practice of separating children from their parents at the southern border among them. “If you think that’s going low — to talk about those issues and to talk about them over and over and over when Donald Trump wants to make jokes, wants to go somewhere else — then I just don’t see it that way.”

On the controversy over reuniting children and parents separated at the southern border, Warren chided the administration for being incompetent.

“This is obviously not a priority for the Trump administration and they clearly don’t have the competence to execute on it,” said Warren, who last month visited a facility on the southern border where illegal immigrants were being detained.

During the interview, Warren also explained why she’s calling to replace Immigration and Customs Enforcement (ICE), which she accused of having a “broken culture. She also touched on Trump’s pending Supreme Court pick to replace Justice Anthony Kennedy and the administration’s handling of North Korea.