The R.E.M.E. unit appears to be one of the first of its kind organized in a local police department, and its creation underscores the urgency with which law enforcement views the threat of far-right inspired attacks. According to the Anti-Defamation League, which tracks such incidents, 50 people were killed by extremists in the United States in 2018, and every one of the incidents was linked to far-right ideologies.

The unit will use the same tools that are applied in other terrorism investigations, said Thomas Galati, the chief of the department’s intelligence bureau. In an interview, Mr. Galati declined to go into specific detail. But police officials said those tools could include anything from tracking internet message boards to undercover operations inside far-right groups.

The city’s police department had previously investigated threats from such organizations across several different divisions. But one week this summer rattled police officials in New York: A gunman in El Paso, Texas, opened fire in a Walmart and killed 22 people; a separate shooter in Gilroy, Calif. shot and killed three at a Garlic festival; and another shooter in Dayton, Ohio opened fire in a bar and killed nine.

Those three incidents prompted the department to expedite creation of the new unit, the police said.

“You can wait for that terrible thing that has a terrible impact on human life to happen in New York City,” Mr. Miller said. “Or you can look at those things that are happening in all those other places and say, ‘Let’s organize a more focused effort to detect and prevent that now.’”

The size of far-right groups in New York City remains unclear. Katherine Sizemore, an intelligence analyst assigned to the new unit, said that while few of them are based in New York, the city is often mentioned as a target for attacks.

“Who do they see as being the threat to the society they want to create — this white ethnostate?” Ms. Sizemore said. “A city like New York City, where you have all of these races and ethnicities and religions all in one place. That’s the threat.”