WASHINGTON (CNN) — New Jersey Lt. Gov. Kim Guadagno on Monday called allegations that she issued an ultimatum to Hoboken's mayor to support a redevelopment plan backed by Gov. Chris Christie or lose Hurricane Sandy recovery aid "false" and "illogical."

"Mayor (Dawn) 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. Any suggestion that Sandy funds were tied to the approval of any project in New Jersey is completely false," Guadagno said at a Martin Luther King Jr. holiday service project in Union Beach, New Jersey.

Guadagno's denial flies in the face of allegations by Hoboken Mayor Dawn Zimmer, who said Sunday that Guadagno told her to support a redevelopment project backed by Christie or lose Sandy recovery funds for her city.

Zimmer's accusation

Zimmer said Guadagno approached her in a parking lot after a May political event. She alleged recovery funds hinged on her support of a real estate project by the Rockefeller Group, which has ties to the Christie administration.

Appearing Sunday on CNN's "State of the Union," Zimmer said Guadagno told her the message was coming directly from the governor.

"She said that to me -- is that this is a direct message from the governor," Zimmer said.

It's "stunning" and "outrageous," but true, the Hoboken mayor told CNN's Candy Crowley. "I stand by my word."

Zimmer met with the U.S. attorney's office for several hours at its request Sunday and provided the office with her journal and other relevant documents.

"As they pursue this investigation, I will provide any requested information and testify under oath about the facts of what happened when the lieutenant governor came to Hoboken and told me that Sandy aid would be contingent on moving forward with a private development project," she said.

Guadagno's version

The lieutenant governor said she recalls having a conversation with Zimmer that day, but she remembers Zimmer arguing that Sandy recovery aid and redevelopment were the same issue, according to a source close to Guadagno who was not authorized to speak publicly.

Related:

NJ mayor: Sandy aid ultimatum came from Christie

The Democratic mayor of a town severely flooded by Superstorm Sandy said Sunday that she was told an ultimatum tying recovery funds to her support for a prime real estate project came directly from Republican Gov. Chris Christie, a claim a Christie spokesman called "categorically false."

"Kim remembers in their conversation that she was talking about redevelopment and making investments in Hoboken. She remembers Zimmer pressing Kim for money for Sandy. Kim remembers saying you can't tie the two together," the source said. "And she remembers Zimmer continuing to press and showing her a map of the city and pressing for aid for Sandy."

Guadagno spoke Monday in front of mayors whose towns were also affected by Sandy in remarks that appeared carefully planned to discredit Zimmer's allegations. "Frankly, I'm surprised that Mayor Zimmer has chosen to mischaracterize a conversation I had with her about development and job creation in Hoboken," Guadagno said.

Christie administration pushes back

Zimmer's allegations mark the first time an official has connected Christie directly to one of three recent controversies.

Christie spokesman Colin Reed said the accusation that relief funds were withheld is "categorically false."

"It's very clear partisan politics are at play here as Democratic mayors with a political ax to grind come out of the woodwork and try to get their faces on television," Reed said in a statement.

The allegations come as other controversies revolve around Christie's administration. In one, evidence mounts showing that Christie aides were involved in tying up traffic in Fort Lee, a town at the foot of the George Washington Bridge, in what may have been an act of political retribution against another mayor. In another, the Christie administration hired a firm for post-Sandy tourism ads that cost nearly twice as much as the next highest proposal.

The governor's spokesman also said the mayor and governor have had a "productive relationship," noting an August tweet by Zimmer saying she's "very glad Governor Christie has been our Gov."

A different account

Zimmer admitted to supporting Christie in the past, saying she is not a part of "the Democratic machine." But the information around the George Washington Bridge scandal — involving lane closures at the entrance to the busy bridge, apparently for political retaliation — prompted her to speak. She said she sees parallels between her story and the bridge controversy: "The Christie administration using their authority to try and get something."

Her comments over the weekend are a change from what she told CNN last week when she said that while she wondered whether Sandy aid funds were being withheld because she didn't endorse the governor's re-election, she concluded that "I don't think that's the case."

"I don't think it was retaliation, and I don't have any reason to think it's retaliation, but I'm not satisfied with the amount of money I've gotten so far," Zimmer told CNN last week, not mentioning her concerns about the redevelopment project.

But Sunday morning, Zimmer told CNN's Crowley that she didn't speak out before because she didn't think anyone would believe her, adding that she is now "offering to testify under oath."

CNN received images of journal entries that Zimmer told CNN she wrote at the time. In one, Zimmer writes the conversation with Guadagno left her upset and shattered the image she had of Christie.

"I thought he was honest, I thought he was moral — I thought he was something very different. This week I found out he's cut from the same corrupt cloth that I have been fighting for the last four years. I am so disappointed — it literally brings tears to my eyes," the journal entry says.

"I believe if and when (Guadagno) is asked to testify under oath, the truth will come out, because I believe she will be truthful and she will tell the truth," Zimmer told Crowley.

Sandy recovery funds

After Sandy, Hoboken was 80 percent underwater. Zimmer told CNN last week that Hoboken received about $300,000 of the roughly $100 million in state funds the city requested for flood prevention.

Reed, Christie's spokesman, told CNN Hoboken has been approved for nearly $70 million in aid.

Zimmer, however, had a different perspective of allocated funds. She said the $70 million given to Hoboken was through flood insurance and other mechanisms that did not need approval from the state.

Debate about redevelopment

Zimmer's allegations center around a property owned by the Rockefeller Group, which had its plan for "redevelopment" of a three-block area of Hoboken rejected by the city's planning board. Instead, the panel voted to classify the area owned by the company as available for "rehabilitation." The "redevelopment" label was sought because its tax incentives offered a much more lucrative deal for the development company.

Aides and advisers to Christie have ties to Wolff & Samson, the law firm representing the Rockefeller Group.

Wolff & Samson lobbyist Lori Grifa was a former commissioner of the New Jersey Department of Community Affairs, and Wolff & Samson's David Samson is chairman of the Port Authority of New York and New Jersey and was appointed by Christie. Samson was recently served with a subpoena in the George Washington Bridge case by an investigative committee seeking relevant documents.

Another investigation?

The chairman of the investigative committee tasked with looking into the George Washington Bridge scandal weighed in as news of the allegations spread.

New Jersey Assemblyman John Wisniewski, D-Middlesex, told CNN: "This certainly has attracted our attention. We need to obtain all relevant facts, confer with our special counsel and determine the committee's best course of action."

CNN's Chris Frates and Steve Kastenbaum contributed to this report.

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