Clinton did not mention the email issue, instead tossing barbs at Donald Trump and other Republicans.
"Today, the party of Lincoln is the party of Trump," Clinton said to one of several standing ovations.
Former Maryland Gov. Martin O'Malley used his turn on the dais to accuse the Democratic leadership of a "rigged" primary debate process designed to stifle competition.
Despite protests from O'Malley and independent Vermont Sen. Bernie Sanders, who also is seeking the Democratic nomination, DNC Chairwoman Debbie Wasserman Schultz has sanctioned six debates, four of them before the first votes are to be cast in Iowa's caucuses.
"We are the Democratic Party, not the undemocratic party," O'Malley said, standing just a few feet from Wasserman Schultz.
He did not mention Clinton by name, but it was clear that he believes fewer debates will make it harder for underdogs to overtake her.
With Trump and other Republicans getting headlines with inflammatory rhetoric about immigration, O'Malley said, additional debates would help Democrats counter it.
"Will we let the circus run unchallenged on every channel while we cower in the shadows under a decree of silence in the ranks? Or will we demand equal time to showcase our ideas?" O'Malley asked. "Silence and complacency in the face of hate is not an honorable option for the Democratic Party."
At a news conference later, O'Malley said that he believes the party establishment wants to ensure Clinton's nomination. As he left the stage, there was an awkward moment as he and Wasserman Schultz shook hands and spoke. Asked what she said, O'Malley responded, "She said, 'Thanks for coming.' "
Sanders, a socialist who has drawn massive crowds around the country and is averaging about a quarter of the vote in national polls, compared with just under 50 percent for Clinton, said his focus on economic inequality was the only way to inspire a big enough turnout to win.
"What we need is a political movement prepared to take on the billionaire class and create a government that works for all of us and not just corporate America and a handful of the wealthiest people in the country," Sanders said.
"We should have a candidate who takes on the establishment, not one who is part of that establishment," he said.
Former Rhode Island Gov. and U.S. Sen. Lincoln Chafee, a former Republican, stressed his opposition to the Iraq war in 2003, compared with Clinton's support.
"In more than 30 years of public service, I have never had a scandal - and that's not easy in Rhode Island," Chafee said. It was an apparent reference to the email imbroglio, though Chafee later told reporters he hadn't meant a "swipe" at anyone.
Clinton paid homage to Democratic goals such as a raise in the minimum wage, equal pay for women, an easing of college debt, better access to child care, affordable health care, paid family leave, and equal rights for gays.
"My whole life, I've worked to even the odds for those people who have the odds stacked against them. That's what we Democrats do," said Clinton, who interrupted a vacation in the Hamptons to attend the meeting.
She also promised that she would help elect Democrats up and down the ticket, addressing persistent complaints from state party leaders that they have been starved for resources under the Obama administration.
"It's time to rebuild our party from the ground up, and if you make me your nominee, that's exactly what I will do," she said.
With Vice President Biden considering a run for the nomination, Clinton's campaign leaked that it had already locked down the support of 440 "superdelegates," party leaders who are automatically seated at the convention - about 20 percent of the total needed to win.
At a news conference, she declined to comment on the number but did not deny it.
"This is really about how you put the numbers together to secure the nomination," Clinton said, adding, in a reference to her 2008 campaign. "As some of you might recall, I got a lot of votes last time, but I didn't get enough delegates."
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