The allegation first surfaced on Saturday when Ms. Zimmer, in an interview on MSNBC, said that the threat was made by Ms. Guadagno in a parking lot in May. Ms. Zimmer said Ms. Guadagno told her that federal Hurricane Sandy recovery funds and money for fortifying her city against another storm would depend on her support for the development project. The mayor said Ms. Guadagno said that Gov. Chris Christie had sent her to deliver that message because the project was so important to him.

Late on Sunday, Ms. Zimmer said in a statement that she had been interviewed about her accusations earlier in the day by prosecutors in the office of the New Jersey United States attorney, Paul J. Fishman, and provided them with documents, including a diary in which she had memorialized her encounter with Ms. Guadagno.

Mr. Fishman’s office was already conducting a preliminary review of allegations that several of Mr. Christie’s aides and appointees, including his deputy chief of staff, had ordered the closing of two approach lanes to the George Washington Bridge in what was apparently an act of political retribution. A spokeswoman for Mr. Fishman’s office, Rebekah Carmichael, would neither confirm nor deny that Ms. Zimmer had been interviewed and declined to comment on her assertions.

On Monday, Ms. Guadagno disputed Ms. Zimmer’s account of their meeting, and denied she had made any threat in connection with the large commercial development project, which was to be on property owned by the Rockefeller Group, which is represented by the law firm of one of Mr. Christie’s closest associates, David Samson.

“Mayor Zimmer’s version of our conversation in May of 2013 is not only false, but is illogical and does not withstand scrutiny when all of the facts are examined,” Ms. Guadagno said at an event to commemorate the Rev. Dr. Martin Luther King Jr.’s birthday. “Any suggestion that Sandy funds were tied to the approval of any project in New Jersey is completely false.”