Addressing the mayor in a video statement this week, Netanyahu said he was going to New York "to tell the truth about our heroic soldiers" and "to tell the truth about you".
He falsely accused Mamdani of supporting Hamas militants.
Mamdani campaigned for office on a promise to have Netanyahu arrested for alleged war crimes should he visit the largest US city, though he later said he determined he lacked the legal authority to do so.
This week, Mamdani described Netanyahu as "the architect of a horrific genocide against Palestinians".
Netanyahu, who rejects war crimes allegations, will be making his first visit to New York since Mamdani took office in January.
Opinion polls suggest an Israeli general election on October 27 could end Netanyahu's long hold on power.
The campaign is unfolding amid mounting criticism of Israel's Gaza war and without a planned meeting with US President Donald Trump.
"He's not really speaking to the UN, he's speaking to the Israeli public," said former Israeli ambassador Michael Oren, who expects Netanyahu's address to resemble a "campaign speech".
"Maybe he's thinking, 'If I can attack Mamdani and attack the Iranians, somebody who was wavering between voting for me and voting for (Gadi) Eisenkot may decide to vote for me'," Oren said, referring to former military chief Eisenkot, Netanyahu's leading rival.
Netanyahu is making an unusually short visit to the US for his UN address.
After arriving early on Thursday, he is expected to fly back the same day after delivering his speech.
Netanyahu is expected to meet some fellow world leaders, but he is not expected to meet Trump.
The two men jointly launched a war on Iran on February 28, but they found themselves on a collision course after the US and Iran agreed to an interim ceasefire that Netanyahu opposed.
Many Israelis were angered by that deal, and opinion polls showed they questioned Trump's commitment to Israeli security, even as his administration proceeds with billions of dollars in arms sales to Israel's government.
Israel has faced deepening diplomatic isolation since launching its war in Gaza in response to the Hamas-led attacks on Israel nearly three years ago.
Netanyahu is unable to travel to many countries because of an International Criminal Court arrest warrant, issued against him and his defence minister as well as the leader of Hamas in 2024.
