After entering the stage to a Bruce Springsteen song — “We Take Care of Our Own” — and an introduction from International Brotherhood of Electrical Workers President Lonnie Stephenson, Biden looked out at the audience and smiled about their interaction.

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“I just want you to know,” he said. “I had permission to hug Lonnie.”

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The crowd of mostly white men inside the Washington Hilton laughed and applauded.

Later, partway through his speech, Biden spotted a quartet of children walking through the middle of the ballroom and invited them onto the stage. He shook each of their hands; then he put his arm around one of the young boys.

“By the way, he gave me permission to touch him,” he joked again. It did not appear that Biden and the boy exchanged words beforehand.

The labor event marked Biden’s first public appearance since the seven women went public, in various forums, about their uneasiness with Biden’s conduct. Biden recorded a video on Wednesday saying that he would work on his demeanor.

Throughout his nearly five decades in public life, Biden has indulged a personal style in which he regularly dispenses hugs, holds hands, and presses his forehead against someone else’s. But in the era of #MeToo, those interactions have been cast in a new light.

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A former Nevada state legislator, Lucy Flores, wrote last Friday that she felt uncomfortable during an encounter with Biden in 2014 in which he held her shoulders, smelled her hair, and kissed her head. At least six other women later came forward with similar accounts, as others have written about their own more positive experiences with Biden.

On Friday afternoon, after Biden’s joking remarks, Flores responded to Biden on Twitter.

“It’s clear @JoeBiden hasn’t reflected at all on how his inappropriate and unsolicited touching made women feel uncomfortable,” she wrote. “To make light of something as serious as consent degrades the conversation women everywhere are courageously trying to have.”

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Amy Lappos, a woman from Connecticut who recounted earlier in the week an instance in which Biden rubbed noses with her, also found his response troubling.

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“Biden’s consent joke is a clear indication Biden doesn’t get it and doesn’t take the voice of the women who have come forward seriously,” she told The Washington Post. “A man who jokes about consent isn’t on the right side of women’s issues. This was also a joke about consent from a child, which adds a new level of creepy and gross.”

Minutes after his labor speech ended, Biden addressed reporters outside the hotel.

“It was not my intent to make light of anyone’s discomfort,” he said. “I realize my responsibility is to not invade the space of anyone who is uncomfortable in that regard. And I hope it wasn’t taken that way.

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“I literally think it is incumbent upon me, I think everybody else, to make sure that if you embrace someone, if you touch someone, it’s with their consent — regardless of your intentions, if you’re trying to bring solace, if you’re trying to welcome them. And it’s my responsibility to do that.”

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He said he wouldn’t be surprised if more women came forward. But asked whether he owed the women an apology, he avoided a direct answer.

“Well, look, I — the fact of the matter is I made it clear that if I made anyone feel comfortable, I feel badly about that. That was never my intention. Ever. Ever. Ever.”

When reporters said that some of the women had said they just want to hear that he is sorry and acknowledges his fault, he declined to do so.

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“I’m sorry I didn’t understand more,” he said. “I’m not sorry for any of my intentions. I’m not sorry for anything that I have ever done. I have never been disrespectful intentionally to a man or a woman. You know, that’s not the reputation I had since I was in high school for God’s sake.”

Biden is widely expected to enter the presidential race, with some aides forecasting an announcement by the end of this month. He was captured Thursday in a photo outside his childhood home in Scranton, Pa., one indication that he could be preparing a video to announce his campaign.

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Biden all but announced he would be running while speaking with reporters.

“I’m told by the lawyers that I’ve got to be careful what I say so that I don’t start a clock ticking and change my status,” he said. “But it is — I am very close to making a decision to stand before you all relatively soon.”

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Asked about the delay, he said, “What’s the holdup? Putting everything together, man. Putting everything together.”

He also said that, strategically, he always wanted to be the last person to get into the race.

“Give everybody else their day; then I get a shot, and then we’re off to the races,” he said.

Asked whether the party had moved too left for him, Biden said, “We’ll find out whether I can win in a primary.”

President Trump has relished Biden’s struggles. Despite being accused by more than a dozen women of sexual misconduct, Trump taunted Biden on Thursday by tweeting a doctored video of the former vice president.

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“I see that you are on the job and presidential, as always,” Biden responded on Twitter.

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Trump has repeatedly denied charges of misconduct that stretches back decades. In a 2005 tape from “Access Hollywood,” which The Post obtained in October 2016, Trump was captured saying that he could “grab” women by their genitals. “When you’re a star, they let you do it,” he said. “You can do anything.”

“I think I’m a very good messenger, and people got a kick out of it,” Trump said of Biden to reporters on Friday. “He’s going through a situation; let’s see what happens. But people got a kick . . . we gotta sort of smile a little bit, right?”

The scrutiny of Biden’s past behavior in a new light is only one of the challenges he may face if he enters the presidential race. Since Biden last ran for president on his own in 2008, the Democratic Party has shifted dramatically in recent years, with much of the energy being guided by millennials, women and people of color.

Biden has tried to answer for some of those past positions — including his handling of Anita Hill’s testimony during Supreme Court Justice Clarence Thomas’s confirmation hearing — but many activists believe he has not gone far enough.