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“This one is not a close call and I think it is why you see some Democrats and their co-agents and some of the mainstream media publications calling for an investigation,” Conway told "America's Newsroom."
Conway said that Biden needs to “unseal” the records at the University of Delaware and “let us go through them.”
“You should unseal them anyway if you want to run for president," she added, referring to the potential existence of a document referring to a complaint that Biden's former Senate staffer claims to have filed about the incident.
"They aren’t true. This never happened," Biden said in a written statement put out by his campaign on Friday.
"While the details of these allegations of sexual harassment and sexual assault are complicated, two things are not complicated. One is that women deserve to be treated with dignity and respect, and when they step forward they should be heard, not silenced. The second is that their stories should be subject to appropriate inquiry and scrutiny."
Further, Biden called for the secretary of the Senate to ask the National Archives to "identify any record of the complaint she alleges she filed and make available to the press any such document.
"If there was ever any such complaint, the record will be there," he said, while stressing that Senate staffers she complained to have said they have no knowledge of this. Biden also said the Archives are the relevant entity, and not the University of Delaware, which has many of his Senate papers but does not contain "personnel files."
Conway highlighted the inconsistencies after left-wing “feminists” argued in the past that all accusations of sexual assault should be believed, most notably concerning the accusations against Supreme Court Justice Brett Kavanaugh.
“'Believe all women' means all women. Not just based on who they are, what their station in life is, whether they have a college degree, if they’re Democrat, Republican, independent or not registered to vote. It doesn’t matter when you said believe all women. I saw no footnotes, no asterisks.
“It is very difficult, as the feminists have said at the time, for women to come forward," Conway continued. "If it’s open and shut now because Joe Biden said it’s not true, you are silencing millions of more women.”
Fox News' Tyler Olson and Morgan Phillips contributed to this report.