White House press secretary Jen Psaki on Monday said President Biden supports the investigation into the sexual harassment allegations leveled against New York Gov. Andrew Cuomo, maintaining that "every woman" who comes forward be treated with "respect."

Psaki's comments come as Cuomo is facing pressure from both sides of the aisle after two former aides accused him of sexual harassment. Cuomo, on Sunday, agreed to an investigation into the matter led by New York Attorney General Letitia James.

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"Every woman coming forward should be treated, treated with dignity and respect," Psaki said Monday. "That applies to Charlotte. That applies to Lindsay and any woman coming forward." 

Last week, former Cuomo aide Lindsey Boylan published a blog post, accusing the governor of unwanted kissing and touching and inappropriate comments.

Boylan accused the governor of going "out of his way to touch me on my lower back, arms and legs," kissing her while they were alone in his office, and suggesting that they "play strip poker" during a plane ride.

Cuomo's office denied Boylan's harassment claims, calling them "simply false" and insisting the strip poker comment "did not happen."

Over the weekend, former Cuomo adviser Charlotte Bennett also came forward, saying the governor asked her questions about her sex life, whether she was monogamous in her relationships and if she had ever had sex with older men.

The 25-year-old staffer described to the New York Times an incident that took place in June when she was "alone" with the 63-year-old governor in his State Capitol office. According to the report, he allegedly asked her if she thought age made a difference in romantic relationships and that he was open to having relationships with women in their 20s, which were noted by the Times as "comments she interpreted as clear overtures to a sexual relationship."

In response to the allegations, Cuomo told the Times that he "never made advances toward Ms. Bennett nor did I ever intend to act in any way that was inappropriate."

Psaki, on Monday, pointed to James' announcement from Sunday, that she would oversee an independent investigation with subpoena power. 

"The governor's office said he will fully cooperate," Psaki said. "We certainly support that process and we'll wait to see that through." 

Psaki added that Bennett's story, over the weekend, was "incredibly uncomfortable to read as a woman." 

"And we certainly believe that every woman coming forward, Charlotte, Lindsay, have should be treated with respect and dignity and be able to tell their story and treated with respect," Psaki said. "There is a process of reviewing... an independent investigation." 

She added: "We will leave it to that process through the attorney general to make a determination on the path forward." 

Psaki was asked whether there was a "red line"' for the Biden administration with regard to harassment allegations, and whether questions about someone's personal or romantic life that made an individual uncomfortable would be grounds for resignation from the administration. 

"The president has a bar for what is expected in his administration, which you referenced, treating people with civility, treating people with respect," Psaki said. "And that's what bar he holds in his administration."

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Psaki, doubled down, saying that "in terms of the path forward and the outcome of the investigation, we will leave it to the attorney general and others to conclude that." 

Cuomo agreed to be subjected to an investigation, but that led to controversy when he first appointed former federal Judge Barbara Jones to lead the probe. Jones was a former law firm colleague of former Cuomo aide Steve Cohen. Following criticism over this pick, Cuomo's office announced the selection of Court of Appeals Chief Judge Janet DiFiore to work with New York Attorney General Letitia James to select an independent lawyer for the probe.

James rejected that plan.

"The state's Executive Law clearly gives my office the authority to investigate this matter once the governor provides a referral," James said in a statement. "While I have deep respect for Chief Judge DiFiore, I am the duly elected attorney general and it is my responsibility to carry out this task, per Executive Law."

Cuomo eventually agreed to this.

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"The governor's office wants a thorough and independent review that is above reproach and beyond political interference," Cuomo's special counsel Beth Garvey said in a statement. "Therefore, the governor's office has asked Attorney General Tish James to select a qualified private lawyer to do an independent review of allegations of sexual harassment."

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On Sunday, Cuomo said in a statement that while at work he likes to "make jokes that I think are funny," and has "teased people about their personal lives, their relationships, about getting married or not getting married." The governor claimed that he did not mean to offend anyone, but recognized that he now sees "that my interactions may have been insensitive or too personal and that some of my comments, given my position, made others feel in ways I never intended."

Cuomo added: "I acknowledge some of the things I have said have been misinterpreted as an unwanted flirtation."

Fox News' Ronn Blitzer contributed to this report.