A third woman has accused New York Governor Andrew Cuomo of inappropriate behavior, just hours after the he referred himself for investigation over similar allegations from two former aides.

Mr Cuomo has faced growing criticism, including from within his own Democratic Party, for suggesting the two ex-aides had "misinterpreted" him.

Anna Ruch, 33, told The New York Times that she met Mr Cuomo at a wedding in September 2019. During the reception, he put his hand on her bare lower back - which she pushed away - and asked if he could kiss her.

"I was so confused and shocked and embarrassed," Ms Ruch told the Times. "I turned my head away and didn't have words in that moment."

Mr Cuomo became a national star last spring with his straight-talking yet empathetic coronavirus briefings that contrasted sharply with then-president Donald Trump's dismissive approach to the pandemic.

Ms Ruch's testimony comes just days after former aide Charlotte Bennett told The New York Times that he sexually harassed her last year.

Ms Bennett's allegations on Saturday came just four days after another ex-aide, Lindsey Boylan, described unwanted physical contact from Mr Cuomo.

Yesterday, New York Attorney General Letitia James said that Mr Cuomo's office had written to her granting her request to set up an independent inquiry into the accusations.

"This is not a responsibility we take lightly as allegations of sexual harassment should always be taken seriously," Ms James said in a statement.

The referral letter noted that the findings of the investigation will be "disclosed in a public report," Ms James added.

On Sunday Mr Cuomo, 63, said he was "truly sorry" if his conduct had ever been "misinterpreted as an unwanted flirtation" as he faced mounting pressure over the scandal.

He has denied ever inappropriately touching or propositioning anyone.

He bowed to pressure to grant an independent investigation, initially choosing a former federal judge to lead the probe but high-profile figures in his own party said that was insufficiently transparent.

New York City Mayor Bill de Blasio criticised Mr Cuomo's statement responding to the allegations.

"That's not an apology. He seemed to be saying, 'Oh, I was just kidding around.' Sexual harassment is not funny. It's serious," said Mr de Blasio, a long-time rival of Mr Cuomo's.

A member of the Sexual Harassment Working Group, a group of former New York parliamentary aides which fights harassment, described Mr Cuomo's comments as "insulting."

"He's not taking any accountability. We have no reason to think he's not going to repeat this behaviour again," Rita Pasarell told the Guardian in comments tweeted by the group.

Ms Bennett described the governor's response as "the actions of an individual who wields his power to avoid justice" in a statement last night to the Times. 

Ms Boylan also tweeted her support, writing that Ms Ruch's account made her "feel sick."

According to the 25-year-old Ms Bennett, Ms Cuomo said 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 reported. 

While Mr 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 Wednesday, Ms Boylan said in a blog that Mr Cuomo had harassed her when she was working for his administration, from 2015 to 2018.

Ms 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." 

Cuomo hires defence lawyer in nursing home inquiry

Separately, Mr Cuomo has retained a prominent white-collar criminal defence lawyer to represent his office in a federal investigation into the state's misreporting of Covid-19 deaths among nursing home residents.

He has come under fire in recent weeks over his office's role in reporting the official count of coronavirus fatalities among patients of nursing and extended-care facilities.

Elkan Abramowitz, a former federal prosecutor now working in private practice in New York City, was hired to represent Mr Cuomo's "executive chamber" - consisting of the governor and his immediate staff - in the US
Justice Department inquiry into the Covid-19 nursing home deaths, senior advisor Rich Azzopardi said.

The governor's brother, CNN host Chris Cuomo, told viewers last night he could not cover stories surrounding the allegations on the governor due to their relationship.

"Obviously, I'm aware of what's going on with my brother," he said. "Obviously, I cannot cover it because he is my brother. Now, of course CNN has to cover it. They have covered it extensively and they will continue to do so."

In January, the attorney general's office issued a report that cast doubt on the Cuomo administration's handling of the coronavirus crisis, saying the state health department significantly undercounted the death toll in nursing homes and implemented policies that may have contributed to it.