But Cuomo, a third-term Democrat, also maintained that he never inappropriately touched or propositioned anyone, denying the allegation of a former aide that he had kissed her on the lips after a one-on-one briefing.
In backing down from his initial positions, Cuomo -- who over a decade in office has kept a powerful grip on the workings of the state government -- signaled an understanding of the severity of a scandal that could threaten his job and prospects for reelection next year to a fourth term. The new accusation drew attention from top state elected officials and a call, on CNN's "State of the Union," from White House press secretary Jen Psaki for "an independent review of these allegations." Psaki called them "serious" and said, of the second accusation, it had been "hard to read that story, as a woman."
Cuomo's office had initially selected former federal Judge Barbara Jones to investigate claims of sexual harassment made against the governor by two female former aides, but the choice was publicly rejected by several high-profile New York Democrats, who argued that Cuomo should have no role in shaping the probe.
Beth Garvey, special counsel and senior adviser to the governor, in a statement earlier Sunday then asked James and Chief Judge Janet DiFiore to choose "an independent and qualified lawyer in private practice without political affiliation" to conduct a "thorough review" and issue a report on the matter in an effort to "avoid even the perception of a lack of independence or inference of politics."
But that push, too, was rejected by James, who in a pair of statements of her own made clear the conditions under which her office could conduct an independent probe.
"To clarify, I do not accept the governor's proposal. The state's Executive Law clearly gives my office the authority to investigate this matter once the governor provides a referral," James said.
"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. The governor must provide this referral so an independent investigation with subpoena power can be conducted."
Early on Sunday afternoon, New York Sen. Kirsten Gillibrand backed James.
"These allegations are serious and deeply concerning. As requested by Attorney General James, the matter should be referred to her office so that she can conduct a transparent, independent and thorough investigation with subpoena power," Gillibrand said in a press release.
She interpreted the exchange -- which she said took place in June while the state was in the throes of fighting the pandemic -- as what the newspaper called "clear overtures to a sexual relationship." CNN has reached out to Bennett for comment on the latest accusation, which the governor denied in a statement on Saturday.
"The last thing I would ever have wanted was to make her feel any of the things that are being reported," Cuomo said, saying that "she came to me and opened up about being a sexual assault survivor" and that "I tried to be supportive and helpful."
Boylan alleged in the Medium post that Cuomo invited her to "play strip poker" during a 2017 flight on his taxpayer-funded jet while another aide was seated beside her and a state trooper behind her. In 2018, Boylan said, Cuomo stunned her by kissing her on the lips after a one-on-one briefing on economic and infrastructure projects in his New York City office.
Cuomo denied Boylan's allegations in a December news conference when she first made them.
In a statement released by the governor's press secretary on Wednesday, four other people said they were on October flights with her and that "this conversation did not happen."
CNN has not been able to corroborate the allegations, and when asked for further comment, Boylan -- who is currently running for Manhattan borough president -- replied that she was letting her Medium post speak for itself. She wrote in the post that she hoped sharing her story "will clear the path for other women to do the same."
This story has been updated with additional developments.
CNN's Maeve Reston contributed to this report.