US intelligence officials alerted joint terrorism task forces of the threat, which also included Texas and Virginia -- though specific sites targeted for Monday in the three states were not mentioned, The New York Post reported, citing a federal source.
Mayor Bill de Blasio said he had learned of the threat several days ago during classified briefings.
"We are still very much assessing the credibility. It is not at all clear how credible this is," de Blasio told WNYC's Brian Lehrer on his weekly radio show on Friday. "We're certainly in a vigilant position."
Hizzoner said the NYPD is planning an "extraordinary" police presence for Tuesday, when Americans go to the polls.
"For the first time in memory there will be two presidential campaigns having their victory celebrations in New York City on Tuesday night," he said, quickly correcting himself that only one candidate will be celebrating.
Republican nominee Donald Trump will be at the New York Hilton Midtown on Sixth Avenue, while his Democratic rival Hillary Clinton will be at the Javits Convention Center across town on 11th Avenue, the report said.
A heavy police deployment had been planned for the New York City Marathon on Saturday, de Blasio said.
Meanwhile, Governor Andrew Cuomo declined to confirm the threat but noted the high state of alert for election day.
"We have more state police, more National Guard, more soldiers on duty than ever before," he said.
"So the bad news is New York is often a threat. The good news is we've been dealing with this now for over a decade and we have prepared for it."
The New York Police Department and the Port Authority of New York and New Jersey said they had been alerted to the possible attacks.
"We are aware of the information. We have been working with the FBI through the Joint Terrorism Task Force and our Counterterrorism and Intelligence Bureaus," the NYPD said in a statement.
"We continue to encourage anyone with any information that could be relevant to the safety of our city to contact law enforcement," the department said.
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