He pledged the concerns would change how he campaigns should he run for president. Biden, who served eight years as vice-president under President Donald Trump's predecessor, Barack Obama, and decades as a US senator, is expected to announce his plans later this month.
Sources close to Biden told Reuters this week that the flap over his history of hugging and touching members of the public at political events has not deterred an expected White House bid.
Biden's remarks on Friday were similar to those he offered in a video he released earlier this week on social media, in which he acknowledged that concepts of "personal space" had changed in the context of the #MeToo movement.
The enduring controversy underscores the challenge the 76-year-old career politician faces should he run.
While Biden consistently sits atop public opinion polls assessing the 2020 Democratic field, some in the party have said he is out of step with its more progressive, diverse and younger elements.
His travails have been noticed by Trump, who on Thursday retweeted a doctored version of Biden's video response to the accusations.
On Friday, Trump told reporters Biden is "going through a situation" and said he doesn't regard him as a political threat.
"I think he's only a threat to himself," Trump said at the White House before departing on a trip to California.
During his speech to the electrical workers union, Biden largely stuck to what is expected to be a persistent theme of his presidential campaign: the vitality of the nation's middle class.
"This country was not built by Wall Street banks, and CEOs and hedge fund managers," he said.
"It was built by the great American middle class."
He criticised Trump, arguing the president undermines the country's core values and is obsessed with settling personal scores.
And, highlighting the tension between Biden and other forces within the Democratic Party, he again complained about attacks from "the far left" over his pledge to work with Republicans should he be elected president.
"How do you get something done?" he wondered aloud.