Former aide Tara Reade recently filed an official police complaint alleging Mr Biden in 1993 pinned her against the wall, reached under her skirt and forced his fingers inside her.
While high-profile Democrats like Hilary Clinton and Elizabeth Warren ignored the allegations when endorsing the presumptive presidential nominee, Ms Pressley said she's "here for an uncomfortable conversation".
In her 600+ word appeal on Medium, Ms Pressley opened up about her own sexual assault while asking Mr Biden and his campaign to "give a response that models the empathy, diligence and acknowledgement of broken systems that this conversation demands".
"I am not new to watching survivors bare their souls, and I am not new to being offered false choices in politics," she wrote in the piece.
"I reject the false choice that my party and our nominee can't address the allegations at hand and defeat the occupant of the White House."
Mr Biden responded directly to Ms Reade's allegations on an episode of MSNBC's Morning Joe program, saying that "believing a woman means taking the woman's claim seriously when she steps forward. And then vet it".
"I don't know what is motivating her. I don't know what is behind any of it, but it is irrelevant. It never happened. It never happened, period," he said.
When asked why he doesn't allow a search for Ms Reade's name among documents at the University of Delaware that could prove whether records of a complaint exist, Mr Biden said information in there could be taken out of context and "be fodder in a campaign at this time".
"There is nothing. They are not there. And I don't understand the point you are trying to make. There are no personnel records by definition," he said.
Ms Pressley, who was elected in 2018 as Massachusetts' first Black congresswoman, said "assumptions and our starting points" for conversations about sexual violence have to change and "the allegations against Joe Biden are no exception".
"Listening to the stories of those who step forward is the baseline. We say 'believe survivors' because, for nearly all of history, the experiences of survivors have been dismissed and derided by a society steeped in misogyny and hatred. We advocate that we begin with assumptions of credibility and move to due process and reconciliation," she said.
"We are in the throes of an election of the greatest consequence -- one that will determine if core rights and tenets of democracy survive in this nation. The stakes cannot be overstated. But I have no patience for any person who tells me that is a reason to lower my voice.
The blog post was backed by her fellow 'Squad' members Rashida Talib and llhan Omar, who said it was a "must read" and that they were "here for it!"
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