She pledged to fight for equal pay for women and address income inequality, and again invoked her husband as an example of economic stewardship.

“When he got into the White House, he realized he had inherited real economic problems from his Republican predecessors — that seems to happen, have you noticed?” Mrs. Clinton said.

But she is not running on her husband’s coattails, she said, as she repeated a popular applause line from her stump speech. “I’m not running for my husband’s third term or President Obama’s third term. I’m running for my first term,” she said, in remarks that ran for about 40 minutes — twice as long as those of other candidates. (One of them, Lawrence Lessig, a professor at Harvard Law School, gently chided her, noting that he would respect time limits for speakers.)

While the crowd applauded the attacks on Republican economic policies, some Democrats in the audience also displayed unhappiness with their own leaders. Scores of them heckled the chairwoman of the Democratic National Committee, Representative Debbie Wasserman Schultz of Florida, over the party’s decision to limit the number of debates for its presidential candidates to six — a decision that one candidate, former Gov. Martin O’Malley of Maryland, said was rigged to help Mrs. Clinton. At points they nearly drowned out Ms. Wasserman Schultz with “More debates!” and “We want debates,” and the chants grew so loud that she went off script and addressed them.

“What’s more important, driving the contrast with Republicans or arguing about debates?” Ms. Wasserman Schultz said. “Let’s focus on our task at hand.”

She then tried to mollify the crowd by attacking a favorite target, the Republican candidate Donald J. Trump, for not correcting a man at a New Hampshire rally on Thursday who said Mr. Obama is a Muslim. The convention hall exploded in cheers, but the party unity did not last long, as the “More debates” catcalls resumed.