“The story of Lawrence is a story about how real change happens in America,” Warren told a crowd that the campaign estimated at 3,500. “It is a story about power — our power — when we fight together.”

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The announcement came after a difficult week for Warren. The Washington Post published a document that shows, for the first time, Warren’s handwritten assertion that she was an “American Indian” on a 1986 registration card she filled out for the Texas bar. Warren in recent days offered apologies for claiming Native American identity, first privately to the leader of the Cherokee Nation and then publicly.

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In forcefully populist language, Warren sought to carve out a distinctive position in the crowded Democratic field, citing achievements like the creation of the Consumer Financial Protection Bureau, which regulates banks and other financial institutions. Other Democrats are also speaking out on inequality, but Warren is hitting particularly hard on the notion of creating new operating rules for the capitalist system.

“It won’t be enough to just undo the terrible acts of this administration,” Warren said. “We can’t afford to just tinker around the edges — a tax credit here, a regulation there. Our fight is for big, structural change.”

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During the roughly 45-minute speech, she repeatedly stressed her image as a fighter, linking her family’s economic struggles to a promise to battle for middle-class Americans. Supporters hope that reputation will eclipse any image of her as someone who misrepresented herself as a Native American for years.

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But even some of those who attended the kickoff had concerns about the strength of her candidacy, given the identity issue and President Trump’s aggressive campaign style.

“Trump is an intimidating guy to take on,” said Hugh Stinson, 40, of Douglas, Mass., before the speech, adding that he hadn’t decided whom to support for president. “Warren has left herself open on a couple fronts to pile on. He loves dredging up Pocahontas,” he added, referencing Trump’s nickname for Warren.

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Others worried that the country isn’t ready for a female president. “I want a candidate who will win. It’s a challenging time,” said Pamela Baldwin, 55, of Arlington, who said she likes Warren as a senator but believes sexism will prevent a woman from becoming president in 2020.

The president tweeted later Saturday about Warren’s decision to enter the race, referencing the Texas bar registration card from 1986.

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“Will she run as our first Native American presidential candidate, or has she decided that after 32 years, this is not playing so well anymore?” wrote the president. “See you on the campaign TRAIL, Liz!”

Trump’s campaign issued a statement Saturday saying Warren has been “exposed as a fraud” by claiming Native American ancestry.

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“The American people will reject her dishonest campaign and socialist ideas, like the Green New Deal, that will raise taxes, kill jobs and crush America’s middle class,” Brad Parscale, Trump’s campaign manager, said in the statement. The Green New Deal, supported by an array of Democrats, is a sweeping environmental initiative.

Warren acknowledged in her speech that some view her ideas as unrealistic. “There will be plenty of doubters and cowards and armchair critics this time around,” Warren said. “But we learned a long time ago that you don’t get what you don’t fight for.”

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Warren was introduced by Democratic Rep. Joe Kennedy, once seen as a potential 2020 presidential candidate himself, and Sen. Edward J. Markey, along with local officials whom Warren has backed.

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Supporters held signs reading “Persist, Persist, Persist,” while some munched on butter cookies with the same word. It became an unofficial Warren motto after Senate Majority Leader Mitch McConnell (R-Ky.), in a 2017 incident, complained that she had been warned against continuing to speak on the Senate floor in violation of Senate rules, but “nevertheless, she persisted.”

After the rally, Warren headed to Dover, N.H., a town of 32,000 with a long history in now-faded industries like shipbuilding. Several of those who braved the biting wind to hear Warren speak at the old City Hall were impatient with the attention on Warren’s Native American ancestry claims.

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“If they are going to toss her out of the ring over that, then they aren’t looking deep enough,” said Sheri Clark Nadell, 58, a high school teacher. “It’s a very superficial way of looking at things.”

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Others cited Warren’s explanation that a Native American background was part of her family lore. “She is in the exact same position as me,” said Fay Scofield, 70. “I was told ever since I was a young child that we are part Native American. I have no idea if it’s true, but it’s always been part of the family story, and we’ve been proud of it. I’m sure she was, too.”

At the Massachusetts event, Warren added some biographical elements, describing herself, as a young mother entering law school, having to quickly toilet-train her toddler so she could leave the child at a day-care center while she attended classes.

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And she blamed the divides in American culture on “the rich and powerful,” saying the country’s problems go beyond the current occupant of the White House.

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Warren has proposed an “ultra-millionaire” tax that adds an annual 2 percent levy on wealth over $50 million and a 3 percent tax on those with assets worth more than $1 billion. She wants large companies to be more tightly regulated, requiring them to focus on more than stock prices and consider their employees and communities. And she wants workers included on corporate boards.

“When I talk about this, some rich guys scream, ‘Class warfare!’ ” Warren said. “Well, let me tell you something — these same rich guys have been waging class warfare against hard-working people for decades. I say it’s time to fight back.”

Warren did not refer to her Native American claims, but she repeatedly mentioned race and the added difficulties confronting minorities. Nonwhite voters made up more than a quarter of the Democratic primary electorate in 2016.

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“Race matters — and we need to say so,” Warren said, noting that blacks continue to face, for example, discriminatory housing practices. “And we can’t be blind to the fact that the rules in our country have been rigged against other people for a long time,” listing women, gays and lesbians, Latinos, Native Americans, immigrants and people with disabilities.

She got some of her biggest applause when she talked about her plan to change politics, repeating a pledge not to take money from special interests. “I’m not taking applications from billionaires who want to run a super PAC on my behalf,” Warren said.

She also backed a constitutional amendment to ensure the right to vote, and she advocated for tightening ethics requirements on members of Congress and even Supreme Court justices.

Warren was the first major candidate to announce a presidential exploratory committee, sending out a video on New Year’s Eve. Since then, the field has grown considerably, including her Senate colleagues Kamala D. Harris (Calif.), Kirsten Gillibrand (N.Y.) and Cory Booker (N.J.). It’s expected to expand further Sunday, with Sen. Amy Klobuchar (Minn.) set to announce her bid.