ALBANY — New York’s Senate rejected Governor Hochul’s nominee to be the state’s chief judge Wednesday, an extraordinary defeat for the state’s top Democrat delivered by legislative leaders in her own party.

The vote rejecting Judge Hector LaSalle as the head of the state Court of Appeals and overseer of New York’s judicial system came after opposition from liberals.

Opponents questioned Judge LaSalle’s decisions as a judge on a midlevel appeals court. Supporters said he was being unfairly targeted by the left and that his judicial opinions were being misconstrued.

Initially, the full Senate had appeared unlikely to even give Judge LaSalle a vote, but its leaders reversed course after a lawsuit filed by a Republican demanded a full vote in the chamber.

Ms. Hochul called Judge LaSalle “an overwhelmingly qualified and talented jurist.” But she said she would make a new nomination.

“I remain committed to selecting a qualified candidate to lead the court and deliver justice. That is what New Yorkers deserve,” she said in a statement.

Senate leaders maintain they fulfilled their legal duty with a panel’s vote last month rejecting Judge LaSalle. But they said they went ahead with a full floor vote to remove an unwanted distraction as they negotiate a $227 billion budget with the governor.

“We have a budget to enact. We have a top court that needs to be fully constituted. And we are taking this matter to the floor today to resolve this crisis,” Senator Michael Gianaris said on the Senate floor.

With Judge LaSalle looking on from a gallery, the Senate rejected his nomination by a vote of 20-39. Democrats overwhelmingly voted against Judge LaSalle. 

Earlier in the day, the Senate Judiciary Committee voted to consider the judge’s nomination for a second time, this time sending it to the full Senate.

A lawsuit filed last week by the ranking Republican on the committee, Senator Anthony Palumbo, claims the state constitution doesn’t give the panel the last word. The lawsuit sought to force a floor vote on the judge.

Mr. Palumbo on the floor Wednesday accused Democrats of gamesmanship in trying to render the court case moot. He said he would press on with the lawsuit, which was to be argued on Friday. 

Mr. Palumbo later said he hoped the lawsuit sets a court precedent that “regardless of what party is in power, nominations need to go to the floor.”

Judge LaSalle, who presides over one of four state appellate districts, was tapped by Ms. Hochul to be the first Latino to lead the seven-member high court.

Progressive activists, labor leaders and liberal senators claimed his record as an appellate judge is too conservative for such an influential position. 

Supporters of Judge LaSalle accuse his critics of unfairly characterizing his views based on a handful of cases to usher in a more liberal judge.

“They don’t want somebody who’s going to follow the law. They want somebody who is going to interpret the law the way they want the law interpreted. That’s not what a judge is supposed to do,” a Republican senator, Steven Rhoads, argued during the debate.

Mr. Palumbo told senators that Judge LaSalle was “a plain-old liberal Democrat.”

The Senate majority leader, Andrea Stewart-Cousins, said she had a good talk on the phone with Ms. Hochul before the vote, and that Democrats are committed to working with the governor on the next nominee.

“I think we have come to the conclusion that we can find a better nominee that can lead this court,” a Democratic senator, Brad Hoylman-Sigal, said on the floor, “and we need to do it ASAP.”