A day after news broke that the actress Cynthia Nixon was in talks with two Democratic strategists about entering the 2018 governor’s race in New York, the two-term incumbent, Andrew M. Cuomo, wasted little time in denigrating her as a second-tier celebrity who had been egged on by his longtime Democratic rival, Mayor Bill de Blasio.

His accusation set off a familiar war of words between Mr. Cuomo and Mr. de Blasio that took on added weight in light of Mr. Cuomo’s possible primary contest.

In a conference call with reporters on Wednesday about a looming snowstorm, Mr. Cuomo laughed aloud at his answer to a question about whether the mayor, a longtime friend of Ms. Nixon, is behind her possible candidacy.

“I think it was probably either the mayor of New York or Vladimir Putin,” Mr. Cuomo said with a chuckle. “I am going to leave it to you, great investigative reporters to follow the facts and ferret out the truth.”