Senator Amy Klobuchar of Minnesota spoke of her grandfather, a union iron ore miner. Former Representative John Delaney of Maryland told the crowd of his father, a union electrician. Senator Elizabeth Warren of Massachusetts said she had helped graduate students, casino workers and airport workers unionize.

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Senator Michael Bennet of Colorado rolled out a new policy plan focused on American workers , particularly those without a four-year college degree. “In this election, it won’t be enough to run against Donald Trump’s lies and empty promises,” Mr. Bennet said. “We need to make crystal clear that the Democratic Party stands for working people.”

The candidates’ speeches also put a spotlight on the continuing divisions over whether to move to a “Medicare for all” system that would eliminate private health insurance — and the ramifications that would have for union members, whose leaders often negotiate generous health care plans with employers at the expense of raising wages or securing other benefits.

Several candidates argued against getting rid of private health insurance — a move supported by Mr. Sanders and Ms. Warren under Medicare for all. Former Vice President Joseph R. Biden Jr., who wants to allow people to keep their private insurance but give them the option of signing up for a government-run health plan, was among those to raise the issue.

“You’ve negotiated really hard for your benefits with your union with the employer,” he said. “And my plan, you get to keep it — you don’t have to give it up.”