“I’m not going to resign,” Cuomo told reporters, in his first appearance since the accusations came to light last week.
The governor apologized for any “hurt” he had caused, adding he now understood that he acted in way that made people feel “uncomfortable.”
“It was unintentional. And I truly, and deeply apologize. I feel awful about it. And frankly, I am embarrassed by it. And that’s not easy to say,” the 63-year-old said.
Cuomo said he would “fully co-operate” with an independent investigation into his conduct being led by New York state Attorney General Letitia James.
He asked New Yorkers to await the outcome of the probe before “forming an opinion on the allegations.”
“Make the decision when you know the facts,” the three-term governor said.
The Democrat has endured a spectacular fall from grace since he became a national star last spring for his handling of New York’s coronavirus pandemic.
Last week former aide Lindsey Boylan described unwanted physical contact from Cuomo when she worked for his administration, from 2015 to 2018.
Boylan, 36, alleged that the governor had given her an unsolicited kiss on the lips, suggested that they play strip poker and went “out of his way to touch me on my lower back, arms and legs.”
“I never touched anyone inappropriately,” Cuomo said, repeating denials that he gave in a statement over the weekend.
“I never knew at the time that I was making anyone feel uncomfortable,” he added.
Days after Boylan’s allegation another ex-aide, Charlotte Bennett, told the New York Times that Cuomo sexually harassed her last year.
Bennett, 25, said that Cuomo told her in June that he was open to dating women in their 20s, and asked her if she thought age made a difference in romantic relationships, the Times said.
While Cuomo never tried to touch her, “I understood that the governor wanted to sleep with me, and felt horribly uncomfortable and scared,” she said.
On Monday, Anna Ruch, 33, told the New York Times that Cuomo had put his hand on her bare lower back — which she pushed away — and asked if he could kiss her during a wedding reception in September 2019.
Democrats and Republicans have joined Cuomo’s accusers and anti-harassment campaigners in calling for Cuomo to step down.