The two have been having been going back and forth for the last week. On Sunday, Trump brought up a long-running controversy surrounding Warren's Native American heritage, telling the New York Times, "I think it's wonderful because the Indians can now partake in the future of the country. She's got about as much Indian blood as I have. Her whole life was based on a fraud. She got into Harvard and all that because she said she was a minority."

>> PHOTOS: Notable supporters of 2016 presidential candidates

Warren went on to tweet Monday that Trump's been able to keep his father's empire going by using corporate bankruptcies to get rid of debt. She also wrote that experts say Trump might have more money if he had just left his inheritance in an index fund.

She then threw another punch.

".@RealDonaldTrump knows he's a loser. His insecurities are on parade: petty bullying, attacks on women, cheap racism, flagrant narcissism," she tweeted.

That tweet has been retweeted nearly 1,000 times.

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The Democratic senator then turned the conversation to the presidential election. She tweeted that just because Trump "is a loser everywhere else, doesn't mean he'll lose the election." Trump is currently leading in the delegate count among the Republican presidential candidates.

Warren said Trump will tear apart the values of America, including "decency, community and concern for our neighbors."

She then referenced history and past authoritarian leaders.

"Many of history's worst authoritarians started out as losers – and @realDonaldTrump is a serious threat," she wrote.

Warren ended the stream of tweets, which were all sent in a period of four minutes, saying that Americans need to help end his campaign.

"The way I see it, it's our job to make sure @realDonaldTrump ends this campaign every bit the loser that he started it," she said.

She also wrote a Facebook post, giving more detail about the election and politics. She asked people to consider what hangs in the balance, listing affordable college, health care and expanded social security.

>> Click here to read the post

"The chance to turn our back on the ugliness of hatred, sexism, racism and xenophobia. The chance to be a better people," she wrote.

Warren has not endorsed anyone in the presidential election.

When asked about Warren's comments during a press conference Monday, Trump said, "Who is that, the Indian? You mean the Indian?"

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>> Watch a video report from Boston's WFXT