Biden says, "I see that you are on the job and presidential, as always."
In his two-minute video released Wednesday, Biden defended past behavior of close contact with women that has come under recent scrutiny, and he said he's 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 CarpeDonktum, who first posted the video on his YouTube channel Wednesday.
In his Twitter bio, he describes himself as an "Eternally Sarcastic Memesmith" and says, "I tweet and meme in support of Donald Trump."
Trump has 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 that 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 on 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 that 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.