Michael Mulgrew, president of the teachers’ union, said he urged the advocacy groups on Friday to have the Working Families Party remain neutral until after the Democratic primary.

If the group endorses Ms. Nixon and she loses the Democratic primary to Mr. Cuomo, she could remain on the ballot through November competing for votes, potentially to the benefit of the Republican nominee.

“My only concern is some reckless behavior that will have an unintended consequence of us ending up with a Republican governor,” Mr. Mulgrew said. “When these elections are over, we will judge any decision we have to make off your behavior if you caused bad things to happen — even though it was not your intent you are responsible for them.”

He declined to comment on whether Mr. Cuomo had asked him to defund community groups backing Ms. Nixon, saying he has “requests on all sides.”

“I’m not going to divulge personal conversations,” he said.

But Bill Lipton, the state director of the Working Families Party, said that he had attended a meeting earlier this week in which the governor had said, “If unions or anyone give money to any of these groups, they can lose my number.”