The Democratic mayor of the New Jersey city of Hoboken has accused the state's Republican governor, Chris Christie, of withholding money for Hurricane Sandy relief work until she approved a redevelopment plan which he supported.

Speaking to MSNBC on Saturday morning, Dawn Zimmer said: “The bottom line is, it’s not fair for the governor to hold Sandy funds hostage for the city of Hoboken because he wants me to give back to one private developer.”

Christie, who has been presumed to be a frontrunner for the Republican presidential nomination in 2016, is already under pressure regarding the allegedly politically motivated closing of traffic lanes on the George Washington bridge between his state and Manhattan.

The Democratic mayor of Fort Lee, Mark Sokolich, who refused to endorse Christie for re-election last year, was allegedly the target of those lane closures. The New York Times has also reported that the Democratic mayor of Jersey City, Steven Fulop, was cut off from Sandy relief and support on other issues after he declined to offer his endorsement.

In the matter of the George Washington bridge, Christie has apologised, fired one of his deputy chiefs of staff and said he had "no knowledge or involvement".

Zimmer, who supported Christie as governor, has not approved the Hoboken building project in question, which would give a New York developer, the Rockefeller Group, the right to redevelop a stretch of land in the city. She told MSNBC two members of the Christie administration warned her that Sandy funds would not be made available until she approved the project.

Hoboken was badly damaged by Hurricane Sandy, which hit the US east coast in October 2012. MSNBC reported that Zimmer requested $127m (£77m) in hurricane relief and was given $147,000 against the cost of one back-up generator for a flood pump, and $200,000 in recovery grants.

In a statement in reply to MSNBC, a spokesman for Christie said: “Mayor Zimmer has been effusive in her public praise of the governor’s office and the assistance we’ve provided in terms of economic development and Sandy aid. What or who is driving her only now to say such outlandishly false things is anyone’s guess.”

In response, Zimmer said: “I’d be more than willing to testify under oath and – and answer any questions and provide any documents, take a lie detector test. And, you know, my question back to them is, ‘Would all of you? Would all of you be willing do that same thing, to testify under oath, to take a lie detector test?’”

On Saturday, as head of the Republican Governors Association, Christie was in Florida to lead fundraising events for Governor Rick Scott. Asked about the effect of the “Bridgegate” scandal, a local GOP fundraiser told the Associated Press: "The jury is definitely now out. He's gone from an A+ to a B. He's not going to be the presidential nominee in waiting. We're in a watch-and-see phase."

Also on Saturday, the Florida congresswoman Debbie Wasserman Schultz, who is chair of the Democratic National Committee, held a press conference near Christie's Orlando fundraising event.

"Republican governors have been touting themselves as the grown-ups and the ones that have the ability to lead us forward," she said. "The guy they chose as their leader is Chris Christie, who has been characterised as a maniacal bully by Republicans and who was willing to take out retribution against not the elected officials who wouldn't endorse him but … his own constituents."

Christie, who prides himself on his ability to work in a bipartisan way, won local and national admiration for his response to Hurricane Sandy, during which he toured affected areas with President Barack Obama, then seeking re-election in a tight race with the Republican nominee, Mitt Romney. In November 2013, Christie was comfortably re-elected.

On Thursday this week, the same day that 20 new subpoenas were issued by a state legislative panel investigating the “Bridgegate” affair, Christie visited Ocean County, to discuss and promote the area's recovery from the affects of Hurricane Sandy.

"I am focused as completely this morning as I was when I woke up on the morning of 30 October 2012,” he said, “and nothing will distract me from getting the job done. Nothing.”

Also on Thursday, Christie announced the appointment of a legal team to deal with multiple investigations into the “Bridgegate” scandal. On Friday, the Associated Press reported that the governor's chief of staff, chief counsel and a top communications aide were among those who received subpoenas the day before.