Mayor Zohran Mamdani recently disclosed that he was in “active conversation” with his legal team about whether he could make good on a campaign vow to arrest Benjamin Netanyahu, Israel’s prime minister, should he set foot in New York City.

What the mayor neglected to say, in a wide-ranging interview with The New York Times last week, was that he had already been advised by lawyers that he had no authority to do so.

His declaration risked a rare public clash with his police commissioner, Jessica Tisch, whose pro-Israel stance runs counter to the mayor’s longstanding position.

Ms. Tisch had no intention of arresting Mr. Netanyahu, and the Police Department was ready to make that clear with a formal statement declaring that it lacked the authority to take such action. Lawyers agreed that such an arrest was not within the scope of the Police Department.

“N.Y.P.D.’s position is entirely rooted in the law,” an agency spokeswoman, Delaney Kempner, said.

Mr. Mamdani quickly pivoted. On Tuesday evening, he released a direct-to-camera message in which he called Mr. Netanyahu a war criminal, but admitted that New York City police officers were powerless to arrest him.