A sexual assault allegation against presumptive Democratic presidential nominee Joe Biden that was largely ignored in the mainstream media when it surfaced last month is starting to attract more attention, earning long stories in both The New York Times and Washington Post in recent days -- but prominent Democrats continue to stay silent on the story, including most of the women who have been discussed as potential vice presidential picks.

The Biden campaign adamantly denies the allegation, as does a former staff member in Biden's Senate office from the time of the alleged incident.

Fox News on Tuesday reached out to the offices of 16 of the women who have been speculated about as possible Democratic vice presidential nominees, including Sens. Kamala Harris, D-Calif., and Elizabeth Warren, D-Mass., as well as Rep. Val Demings, D-Fla., former Deputy Attorney General Sally Yates and several others. None responded as of Wednesday morning.

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Only three of the potential picks have commented publicly on the allegations, all this week. And they generally avoided commenting on the allegations directly.

Sen. Amy Klobuchar, D-Minn., was asked about the allegations in an appearance on NPR Tuesday. She said women have the right to be heard and pointed to investigations by the media into the claims, while touting Biden's past work on behalf of women.

"[I]n this case -- and your listeners should look at the story -- there was a thorough review by The New York Times. And I think that's very important to have, especially involving public figures," she said. "But I think when I look at -- when I see Vice President Biden, someone I worked with, I see him on -- a leader on domestic abuse -- led the bill before people were even willing to talk about those horrific crimes and has really been a champion of abuses of power against women and has used his voice on the domestic abuse front in such a big way."

Sen. Tammy Baldwin, in an interview with the Milwaukee Journal Sentinel on her endorsement of Biden Wednesday, noted that the "allegations are being aired publicly" while saying that she wanted to avoid commenting further until she had read more into the story.

Michigan Gov. Gretchen Whitmer, on NPR Tuesday, made similar comments.

"Well, I think women should be able to tell their stories," Whitmer said, while noting the importance of vetting the allegations. She said "it's hard to give you greater insight than that, not knowing more about the situation."

Biden has been accused of sexual assault by a woman named Tara Reade, who was a staff assistant to Biden when he was a senator. Reade came forward early last year to say that Biden inappropriately touched her -- as multiple women did around that time -- but didn't get much publicity for her story outside of a local newspaper article.

But late last month Reade gave a very different and more graphic account of her interaction with Biden, which allegedly occurred in 1993, that raised the level of the allegation to sexual assault. Reade’s story first resurfaced in an article in The Intercept. She then was interviewed by podcast host Katie Halper, to whom she detailed the alleged assault, including saying that Biden "penetrated me with his fingers and he was kissing me at the same time and he was saying some things to me."

Both the Biden campaign and a former executive assistant to Biden have called the allegation "false."

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"Women have a right to tell their story, and reporters have an obligation to rigorously vet those claims. We encourage them to do so, because these accusations are false," Biden Deputy Campaign Manager Kate Bedingfield said in a statement on the Reade's accusation.

"In all my years working for Senator Biden, I never once witnessed, or heard of, or received, any reports of inappropriate conduct, period -- not from Ms. Reade, not from anyone," Marianne Baker, who worked for Biden's Senate office as an executive assistant from 1982 to 2000, said. "I have absolutely no knowledge or memory of Ms. Reade’s accounting of events, which would have left a searing impression on me as a woman professional, and as a manager. These clearly false allegations are in complete contradiction to both the inner workings of our Senate office and to the man I know and worked so closely with for almost two decades."

Reade filed a report with Washington, D.C., police on Thursday concerning her allegation that Biden penetrated her without consent in 1993. Fox News has confirmed with the District’s police department that she filed the criminal complaint, which does not reference Biden by name.

Reade, who previously openly advocated for Vermont Sen. Bernie Sanders' presidential campaign, has said that she will not vote for Joe Biden in November.

"I will not ever vote in a national election again," Reade said in a statement to Fox News. "Despite the fact I come from a family of Democrats. I worked for Leon Panetta, [California] State Sen. Jack O'Connell and Joe Biden. I worked hard for the Democratic Party as a young woman. It is obvious by the tremendous smears about me leveled by Biden campaign and supporters after I came forward about Biden and the complete lack of support from any Democrat that they care more about protecting Joe Biden than addressing the serious allegations by me and the other seven women who complained about his misconduct."

She continued: "Kamala Harris is my representative and I reached out to her for help. No response. Joe Biden sexually assaulted and harassed me. All the rest of political discussion is noise and an effort to distract from the serious lack of justice I experienced at his hands. Coming forward has been difficult and resulted in 1993 with the loss of my job and career. Coming forward last spring 2019 about the sexual harassment resulted with his supporters smearing me online. And now, again. So, no, I will not vote for Joe Biden."

Despite the Biden denials, the story has moved forward -- if slowly -- in recent weeks.

The New York Times ran a story Sunday which said it could not "corroborate any details of Ms. Reade's allegation" and found no pattern of such behavior by Biden, but also mentioned the paper had spoken to two of Reade's friends who say she had previously told them about the alleged assault.

The Washington Post also ran a long story on the Reade allegations Sunday.

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Also Sunday, former Sanders campaign National Press Secretary Briahna Joy Gray referred to Reade's story as "[c]redible sexual assault allegations" as she listed off a number of issues she believed Sanders "generously" did not raise against Biden during the Democratic primary. She is one of a few scattered liberal voices who are advocating that the Reade allegation be taken seriously, including Rep. Alexandria Ocasio-Cortez, D-N.Y. and liberal activist Rose McGowan.

"As a survivor, the way you launched into this woman’s assault is truly vile,” McGowan tweeted Sunday about the Washington Post story on the Reade allegations. “Your motto is ‘Democracy Dies in Darkness’ well I guess it’s dead because you are dark. Evil lives and it loves the DNC."

"I think it's legitimate to talk about these things," Ocasio-Cortez said while speaking with the women's organization The Wing on Tuesday night, according to CBS News. "And if we want, if we, again, want to have integrity, you can't say, you know — both believe women, support all of this, until it inconveniences you, until it inconveniences us."

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Biden has previously indicated that he thinks women who bring forward sexual assault claims should be presumed to be telling the truth.

"For a woman to come forward in the glaring lights of focus, nationally, you’ve got to start off with the presumption that at least the essence of what she’s talking about is real, whether or not she forgets facts, whether or not it’s been made worse or better over time," Biden told the Washington Post as allegations of sexual assault swirled around the nomination of Justice Brett Kavanaugh to the Supreme Court in 2018. "But nobody fails to understand that this is like jumping into a cauldron."

Biden, however, has not appeared to suffer any political consequences from the Reade allegations so far, securing endorsements from Sanders and former President Obama in recent days even as the accusations swirled.

The former vice president, who has said he will choose a woman to be his VP, has also not gotten any public pushback from his potential vice presidential nominees. It's unclear if that will change as the Democratic National Convention moves closer and the presidential election eventually steals back some media headlines after it has been thoroughly upstaged by the coronavirus pandemic.

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President Trump, who has been the subject of his own sexual assault and harassment allegations in the past, has also not commented on the Reade accusations against Biden.

In addition to Harris, Warren, Demings and Yates, Fox News reached out to 12 other Democrats who have been speculated about as possible running mates for Biden, asking them for comment on the sexual assault allegations against the presumptive nominee.

Fox News reached out to Klobuchar; Whitmer; Baldwin; Sen. Jeanne Shaheen, D-N.H.; Sen. Maggie Hassan, D-N.H.; New Mexico Gov. Michelle Lujan Grisham; Sen. Catherine Cortez Masto, D-Nev.; Sen. Tammy Duckworth, D-Ill.; Sen. Kyrsten Sinema, D-Ariz.; Sen. Kirsten Gillibrand, D-N.Y.; Atlanta Mayor Keisha Lance Bottoms and former Georgia gubernatorial candidate Stacey Abrams through her voter rights organization Fair Fight.

None responded.

Fox News' Brooke Singman, Joseph A. Wulfsohn, Brian Flood, Patrick Ward, Peter Doocy, Adam Shaw and Gregg Re contributed to this report.