The day after Joe Biden posted a video acknowledging that his past behavior had made women uncomfortable, President Trump tweeted a parody video Thursday that shows a second Biden as he approaches the former vice president from behind, puts his hands on his shoulders and appears to sniff his hair.

“WELCOME BACK JOE!” Trump said in the tweet, which he shared with his nearly 60 million followers. Trump’s tweet came after his social media director, Dan Scavino, shared the same video late Wednesday night.

Trump has been accused of sexual misconduct by more than a dozen women. But his tweet Thursday is the latest sign that he intends to escalate his attacks on his potential 2020 White House rival on the issue of his behavior toward women.

Several hours later, Biden hit back.

Retweeting the president, he wrote: “I see that you are on the job and presidential, as always.”

Twitter is Trump’s preferred way to communicate. That Biden engaged with him on the platform seemed like an opening salvo in Biden’s effort to go toe-to-toe with Trump as the Democratic presidential nominee.

In his two-minute video released Wednesday, Biden defended past behavior of close contact with women that has come under recent scrutiny, but also said he is able to change.

“I want to talk about gestures of support that I’ve made to women and some men that have made them uncomfortable,” Biden said, seated on a couch and speaking directly to the camera. “I’ve always tried to make a human connection. That’s my responsibility, I think . . . It’s the way I’ve always been. It’s the way I try to show I care about them and I’m listening.”

The 14-second parody video Trump shared Thursday appeared to have been made by a supporter with the Twitter username Carpe Donktum, who first posted the video on his YouTube channel Wednesday.

In his Twitter bio, he describes himself as an “Eternally Sarcastic Memesmith” and states, “I tweet and meme in support of Donald Trump.”

Trump has previously shared the user’s videos, including a February clip that parodied Democratic reactions to the president’s State of the Union address. That video has since been replaced in Trump’s Twitter feed by a message stating it was disabled by the copyright owner’s request.

Amid mounting allegations that Biden had acted in ways that made women uncomfortable, Trump took aim at the former vice president at a Republican fundraiser in Washington Tuesday night. At one point, Trump told the crowd a story about a conversation he had with a general.

“I said, ‘General, give me a kiss.’ I felt like Joe Biden. But I meant it,” Trump said, prompting laughter from the crowd.

At another point in his remarks, Trump mentioned the 2020 White House race and said the only Democratic candidate who is not a socialist is “being taken care of pretty well by the socialists” — a nod to unproven claims by some Biden supporters that the recent accusations against him are being pushed by his political rivals.

“I was going to say, ‘Welcome to the world, Joe. You having a good time, Joe?’ ” Trump said.

Trump faces multiple allegations of sexual misconduct, including groping and unwanted kissing. The most recent accusation came in February, when Alva Johnson, a former staffer on Trump’s presidential campaign, said Trump kissed her against her will in 2016. Trump has denied all of the allegations against him.

Trump himself spoke graphically about forcibly kissing and groping women during a 2005 conversation that was caught on tape and surfaced during the 2016 campaign.

Colby Itkowitz and Abby Ohlheiser contributed to this report.