Vice President Kamala Harris held a sometimes tense meeting with Teamsters leaders on Monday, defending the Biden administration’s labor policies against pointed questions and concluding with a promise that she would win the presidency and treat the union fairly with or without its backing.

While Ms. Harris has the endorsement of most of the nation’s unions, the International Brotherhood of Teamsters, whose truck drivers, freight workers and other members are divided in their political allegiances, has held out. Sean O’Brien, the union’s combative president, said after the meeting that he could announce an endorsement — if there was an endorsement — as soon as Wednesday.

John Palmer, a Teamsters executive board member and vice president at large, said the meeting had lasted a little more than an hour. He praised Ms. Harris for parrying questions on the role President Biden played in averting a rail strike in late 2022 and the ways the White House could have been more helpful in a Teamsters dispute last summer with United Parcel Service.

Ms. Harris repeatedly castigated her opponent, former President Donald J. Trump, for appointing anti-union members to the National Labor Relations Board when he was president and reminded the Teamsters that Mr. Biden had shored up pensions for thousands of union members.

At the end of the meeting Ms. Harris told the leaders of the union, which has 1.3 million members, “I’m confident I’m going to win this,” according to Mr. Palmer. She also said, “I want your endorsement, but if I don’t get it, I will treat you exactly as if I had gotten your endorsement,” he added — a characterization that Ms. Harris’s campaign aides did not contradict.

After the meeting, Mr. O’Brien said that he still needed time to consider the union’s next move. Ms. Harris opened the meeting by saying she understood she might not get the union’s endorsement, and that some Teamsters would be voting on issues beyond labor, such as the border, according to another person in the room.

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