Fellow Democrats Chuck Schumer and Kirsten Gillibrand said Mr Cuomo had “lost the confidence” of New Yorkers.
Six women have accused Mr Cuomo of unwanted kissing and groping.
On Friday, another woman, a former New York reporter, said Mr Cuomo harassed her.
Mr Cuomo has denied the allegations against him and has defied calls to resign from Democrats.
“I did not do what has been alleged,” Mr Cuomo said before facing the seventh complaint on Friday. “I never harassed anyone, I never assaulted anyone, I never abused anyone.”
In their statement, Mr Schumer, who is also the Senate majority leader, and Ms Gillibrand, said: “Due to the multiple, credible sexual harassment and misconduct allegations, it is clear that Governor Cuomo has lost the confidence of his governing partners and the people of New York. Governor Cuomo should resign.”
Earlier, New York Congresswoman Alexandria Ocasio-Cortez and Congressman Jamaal Bowman also released a joint statement that said, “we believe these women, we believe the reporting, we believe the Attorney General, and we believe the fifty-five members of the New York State legislature,” referring to a group of legislators who have called on Mr Cuomo to resign.
“Governor Cuomo can no longer effectively lead in the face of so many challenges”, the statement said.
New York City Mayor Bill de Blasio, a long-time political rival of Democrat Governor Cuomo, told reporters on Thursday that the latest allegation is “disgusting to me, and he can no longer serve as governor.”
Mr Cuomo, whose term in office comes to an end in 2022, was last year praised for his handling of the Covid epidemic in his state. However, this year he has been accused of obscuring the scale of coronavirus deaths in the state’s nursing homes.
On Thursday, New York State Assembly Speaker Carl Heastie said he had given the go-ahead for an “impeachment investigation” into the allegations made against Mr Cuomo. The investigation, which will interview witnesses and look at evidence, would be the first step towards impeachment.
Mr Cuomo has said he would wait for the results of an independent investigation into the allegations, which is being overseen by New York’s attorney general Letitia James.
What has Cuomo been accused of?
Mr Cuomo was first accused of harassment in February, when Lindsey Boylan, a former top-level aide, wrote in an essay that the governor touched her without her consent and frequently made inappropriate comments about her appearance.
Ms Boylan accused Mr Cuomo of kissing her on the lips and asking her to play strip poker while on his private jet.
Several more women have come forward with allegations. The most serious allegation, that Mr Cuomo groped an unnamed woman beneath her blouse, was referred to police.
In the latest case, Jessica Bakeman, a former statehouse reporter in Albany, accused Mr Cuomo of repeatedly touching her. She wrote in New York magazine: “He uses touching and sexual innuendo to stoke fear in us. That is the textbook definition of sexual harassment.”
Mr Cuomo has yet to comment on the new allegation.