Sen. Kirsten Gillibrand, D-N.Y., told Fox News in an email Sunday that there should be an independent investigation into the sexual harassment allegations that have been leveled against New York Gov. Andrew Cuomo.

Gillibrand, who received some criticism for remaining silent on the allegations, called them "serious and deeply concerning."

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Cuomo acknowledged for the first time Sunday that some of his behavior with women "may have been insensitive or too personal," and said he would cooperate with a sexual harassment investigation led by the state’s attorney general.

In a statement released amid mounting criticism from within his own party, the Democrat maintained he had never inappropriately touched or propositioned anyone. But he said he had teased people about their personal lives in an attempt to be "playful."

Senate Majority Leader Chuck Schumer, the other New York Democrat, said Sunday that he supported state Attorney General Letitia James’ call to lead the probe, according to the Huff Post.

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James said that there "must be a truly independent investigation to thoroughly review these troubling allegations against the governor, and I stand ready to oversee that investigation and make any appointments necessary."

The Associated Press contributed to this report