The message comes just days after Adams, who was elected as a democrat, insisted that he would stand as an independent candidate.
Adams' election campaign has been marked by a corruption charge – which is now closed – where he was accused of, among other things, receiving bribes and illegal campaign contributions from foreign sources.
The withdrawal means that the battle for the mayor's role will likely be between the 33-year-old democrat Zohran Mamdani and New York's former governor, the 67-year-old Andrew Cuomo – who left the governor's post in 2021 after allegations of sexual harassment.