Biden, in an interview and a written statement, adamantly denied the accusation, marking the first response from him on the matter since former Senate staffer Tara Reade leveled the allegation last month.
Abrams, who earlier this week backed Biden in comments published by HuffPost saying that Biden "will make women proud as the next President of the United States," released a statement approving of his "Morning Joe" appearance Friday, according to a Wall Street Journal reporter.
"I am pleased that the Vice President directly addressed these allegations and by how he addressed them," Abrams said. "Women and all people should be heard, and they deserve a safe space and process through which they can come forward."
Abrams' comments come as some potential running mates for the presumptive Democratic presidential nominee have begun going on-the-record about the allegations against him, unable to continue avoiding media questions as Reade's accusations gradually have become a campaign focal point. She says that Biden, in 1993, cornered her and penetrated her with his fingers.
"No, it is not true. I'm saying unequivocally it never, never happened and it didn't. It never happened," Biden said when questioned on the allegation Friday on MSNBC.
Reade, who backed Bernie Sanders in the Democratic primary, has changed her story over time, however. Reade and seven other women had come forward a year prior to accuse Biden of inappropriate contact but the story she told in March was far more graphic, raising the allegation to the level of sexual assault.
But while former Senate aides have pushed back or outright denied the account, a handful of Reade's associates have backed her story, saying Reade told them about the alleged assault previously.
Reade says she filed a complaint against Biden before eventually being forced out of her job in his office, and says the complaint might be in Biden's senatorial papers at the University of Delaware. Biden has said that no such complaint exists, and even if it did, it would be at the National Archives, and has called for a search of the alleged complaint there. He's resisted calls to check the papers at the University of Delaware, which are sealed from the public. It is unclear exactly where the complaint would be if it does exist.
Last month Atlanta Mayor Keisha Lance Bottoms, in an interview with NPR, also strongly backed Biden, like Abrams.
"You know, I don't know much about her story or what her accusations are, but what I do know about Joe Biden is that he is a man of high integrity, and I know that he respects women," Lance Bottoms said. "And so I'm honored that he's our nominee. I know him to be a man of the highest integrity."
Sen. Tammy Duckworth, D-Ill., on Thursday took a slightly less supportive tone than Abrams and Lance Bottoms when asked about the allegation against Biden.
“Any woman who brings, or any man for that matter, who brings forward allegations of abuse, especially in the workplace, deserve to be listened to, and I certainly think that we need to thoroughly look at these allegations,” Duckworth said, according to the Chicago Sun-Times.
Before Biden went on TV, Sen. Jeanne Shaheen, D-N.H., told New Hampshire Public Radio Thursday that she wanted Biden to address the allegations head-on.
"I think it would be important for Vice President Biden to respond to those allegations," she said. "It was a long time ago. Now the details that she has relayed are details that we all should listen to. I think anytime a woman makes an accusation about sexual assault, it's important to take that very seriously. We've seen both The New York Times and The Washington Post have investigated those allegations and at least The New York Times has responded based on their investigation, that they don't see any pattern of behavior."
Sen. Amy Klobuchar, D-Minn., made similar comments last month while also noting that Biden had often backed legislation to help women while a senator.
"[I]n this case -- and your listeners should look at the story -- there was a thorough review by The New York Times," she said in an NPR interview. "And I think that's very important to have, especially involving public figures. 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."
Klobuchar's comments came before a "Larry King Live" video resurfaced showing a woman Reade claims is her mother calling into the show and alluding to her daughter's "problems" working for a prominent senator. The woman on the call never explicitly spoke about sexual assault and never used Biden's name, but the call occurred at a time that corresponds with when Reade says she was forced out of her job with Biden.
Others, including Sen. Kamala Harris, D-Calif., Sen. Kirsten Gillibrand, D-N.Y. and Sen. Tammy Baldwin, D-Wis., have made comments similar to Klobuchar's at a similar time -- before the "Larry King Live" video resurfaced, defending Biden while arguing that sexual assault accusers should be heard.
A spokesperson for Michigan Gov. Gretchen Whitmer told Fox News that the allegations should be taken seriously on the morning after the "Larry King Live" video resurfaced last week.
“Governor Whitmer believes that it is important that these allegations are vetted, from the media to beyond and that it is something that no one takes lightly. But it is also something that is personal. We will not speculate or provide greater insight, without knowing more about the situation," her spokesperson said.
Meanwhile, some of the other potential Biden running mates have still managed to remain silent on the sexual assault allegation.
Rep. Val Demings, D-Fla., Sen. Elizabeth Warren, D-Mass., Sen. Maggie Hassan, D-N.H., Sen. Catherine Cortez Masto, D-Nev., Sen. Kyrsten Sinema, D-Ariz., New Mexico Gov. Michelle Lujan Grisham and former Deputy Attorney General Sally Yates have all not responded to several requests for comment from Fox News over the course of weeks on the allegation against Biden, and Fox News was unable to find public statements on the matter from any of them.
Fox News' Sam Dorman, Dom Calicchio and Brooke Singman contributed to this report.