President Trump on Tuesday floated an outlandish claim that Zohran Mamdani, the Democratic candidate for New York mayor, was an illegal immigrant and threatened to arrest him if he blocked immigration arrests in New York City.

Mr. Mamdani was born in Uganda and has lived in New York City since 1998, when he was 7 years old. He was naturalized as a U.S. citizen in 2018. If elected, Mr. Mamdani would also be the first Muslim to become mayor of New York City. There is no credible evidence to suggest Mr. Mamdani is not, or shouldn’t be, a U.S. citizen.

Mr. Trump’s attack on the mayoral candidate echoed language he has long used to lend credibility to falsehoods. “A lot of people are saying he’s here illegally,” he said of Mr. Mamdani. “We’re going to look at everything.”

When a journalist raised the possibility that Mr. Mamdani “will not allow” ICE to make immigration arrests, Mr. Trump replied, “Well then we’ll have to arrest him.”

“The president of the United States just threatened to have me arrested,” Mr. Mamdani said in a response on social media, adding that Mr. Trump’s statements “don’t just represent an attack on our democracy but an attempt to send a message to every New Yorker who refuses to hide in the shadows: If you speak up, they will come for you.”

He continued, “We will not accept this intimidation.”

Gov. Kathy Hochul, who has so far declined to endorse Mr. Mamdani, rallied behind him after Mr. Trump’s attacks.