Mamdani described the Israeli prime minister as a "war criminal" and said he is not welcome in New York City.
"It is clear that we do not have the independent legal authority to enforce this warrant," he said in a video posted on X.
"The federal government however does and I call on them to join the ICC and execute this warrant," he added, referring to the International Criminal Court.
Mamdani had told the New York Times earlier this month that he and the city's legal department were discussing arresting Netanyahu if he comes to New York City for the UN General Assembly in September.
President Donald Trump on Monday told Netanyahu in a social media post that he "will not be arrested, in any way, shape, or form, while in the United States of America."
The post did not directly mention Mamdani.
Mamdani had said throughout his mayoral election campaign last year that he would seek to order the city's police to arrest Netanyahu under the criminal court's warrant over Netanyahu's role in the war in Gaza.
In his video message, Mamdani said his administration has reviewed all avenues available and determined the city can't execute the arrest warrant.
"I want to be equally clear, Benjamin Netanyahu is not welcome in New York City, nor is any other war criminal at large," he said.
Danny Danon, the Israeli ambassador to the UN, responded by telling the mayor "enough."
"You were elected to serve New Yorkers, not Hamas' propaganda," he said in a statement on social media. "Do your job!"
The world's top war-crimes court issued arrest warrants for Netanyahu and others in 2024, accusing them of crimes against humanity in connection with the war in Gaza.
The ICC said there was reason to believe Netanyahu and former Defence Minister Yoav Gallant have used "starvation as a method of warfare" by restricting humanitarian aid and have intentionally targeted civilians in Israel's campaign against Hamas in Gaza.
Israeli officials deny the charges.
