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A plurality of New York state voters say embattled Gov. Andrew Cuomo should serve out his current term but not seek reelection next year, according to a new poll.

Only a third of voters questioned in a Siena College survey say the three-term Democratic governor should run for reelection next year, with 39% saying he should serve out his term but not seek another four years steering the Empire State, and 23% saying Cuomo should resign immediately.

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Cuomo, who saw his political standing surge last year amid the early stages of the coronavirus pandemic, is facing a state investigation into numerous sexual harassment allegations from former staffers. And the governor is also facing a federal probe into whether his administration covered up the COVID deaths of nursing home residents amid the pandemic. 

"The good news for the governor is that only 23% of New Yorkers want him to resign immediately. However, when you add those voters to the 39% who say he should serve out his term but not seek re-election, 62% say he should not run for a fourth term," Siena College pollster Steven Greenberg said.

Cuomo earlier this year faced a chorus of calls to resign, with more than 135 state lawmakers and nearly the entire congressional delegation from New York – including Democratic Senate Majority Leader Chuck Schumer and Sen. Kirsten Gillibrand – urging Cuomo to step down.

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The governor has been resisting those calls as he continues to emphasize that people should wait for the results of the attorney general's investigation before making up their minds and passing judgment. While he has apologized for making some women uncomfortable, he's denied that he ever inappropriately touched a woman. And Cuomo has criticized some of his accusers who have gone public amid the ongoing investigations of allegations of sexual misconduct, arguing they have impacted the fairness of the process by speaking out. 

New York doesn't have gubernatorial limits, and Cuomo said in May of 2019 that he would run in 2022 for a fourth term. He had built a massive $16.8 million campaign war chest by the beginning of this year, but he’s yet to formally confirm or announce that he’s seeking another term in office.

New York Gov. Andrew Cuomo speaks during a news conference, Wednesday, June 23, 2021, in New York.  Cuomo’s campaign contributors say they’re still planning to donate money for his reelection, despite ongoing investigations into allegations that he sexually harassed employees and manipulated data on COVID-19 fatalities in nursing homes.  (AP Photo/Mary Altaffer)

New York Gov. Andrew Cuomo speaks during a news conference, Wednesday, June 23, 2021, in New York.  Cuomo’s campaign contributors say they’re still planning to donate money for his reelection, despite ongoing investigations into allegations that he sexually harassed employees and manipulated data on COVID-19 fatalities in nursing homes.  (AP Photo/Mary Altaffer)

One telling sign -- the governor hauled in more than $1 million at a fundraiser Tuesday evening at New York City’s Rockefeller Center, a source close to Cuomo’s political circle confirmed to Fox News. The gathering was the most high-profile campaign event the governor has held this year.

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If Cuomo runs, 35% questioned in the poll say they’ll vote to reelect him, while 56% said they prefer someone else. Those numbers are basically unchanged from Siena’s previous poll, conducted in May.

According to the survey, New Yorkers approve of Cuomo’s handling of the pandemic by a 51%-32% margin, but by a 60%-22% margin, they say he did a bad job handling the nursing home COVID crisis. Cuomo’s overall approval/disapproval is underwater at 42%-55%, little changed from last month. And his favorable/unfavorable rating stands at 45%-47%, also little changed from a month ago.

"Since his poll numbers took a significant hit earlier this year, Cuomo’s favorability, job performance and re-elect ratings have remained largely stable the last few months. But 16 months from the next gubernatorial election and less than a year from the primary, only one-third of New Yorkers – including just 43% of Democrats – think Cuomo should run for re-election," Greenberg said.

Besides the federal nursing home investigation and the New York attorney general’s investigation into the sexual harassment allegations, a New York State Assembly committee is looking into the possible impeachment of Cuomo. That committee announced this week that it will begin issuing subpoenas as part of its probe.

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"When it comes to impeachment, voters are more closely divided with 45%, a plurality, saying the Assembly should not impeach Cuomo, while 35% – including one-quarter of Democrats – would like to see the Assembly impeach the Governor," Greenberg said.

The Siena College poll was conducted June 22-29, with 809 New York state registered voters questioned. The survey’s overall sampling error is plus or minus 4.1 percentage points.

Fox News' Tara Prindiville contributed to this report