The former president had been due to be deposed in a civil class action lawsuit first filed in 2018.
It accuses Mr Trump, his children, and the Trump Organization, of committing deception and fraud.
It is different to the lawsuit filed earlier this month by New York Attorney General Letitia James, that similarly accuses Mr Trump and the others of fraud, for allegedly overvaluing his assets by billions of dollars.
The former president has denied any wrongdoing, saying the multiple investigations into him are part of a politically-motivated “witch-hunt”.
Mr Trump was to have been deposed on Friday, but letters filed with a court on Wedneday, and reported by CNN, showed lawyers acting for the plaintiffs told a judge they could not meet a Friday deadline, because he would not move the meeting from his Florida mansion as Hurricane Ian bore down.
John Quinn, one of the lawyers representing a group of people accusing Mr Trump, told a federal judge the former president refused to move his deposition out of Palm Beach.
Mr Quinn and his team did not want to fly into Florida this week given the severity of the storm, and they said Mr Trump’s side would not move the deposition to Bedminster, New Jersey, where Mr Trump has a golf club that he has often made use of.
Mr Quinn wrote that Mr Trump’s lawyer, Clifford Robert, had called him on Tuesday to tell him that the Trump team was boarding a flight to Palm Beach.
“I expressed some surprise — I believe I used the word ‘walloped’ — but Mr Robert indicated they were flying down anyway,” Mr Quinn wrote in his letter.
He said he could not reach Mr Robert and his colleague on Wednesday afternoon.
“Accordingly, the last we heard is that defendants insist the deposition go forward at Mar-a-Lago and on Friday. With all respect, we do not believe that is prudent or safe,” Mr Quinn wrote, attaching a map of Hurricane Ian’s predicted trajectory across Florida.
Hurricane Ian flooding captured on stunning aerial video
The storm has already devastated large parts of Florida around Fort Myers and President Joe Biden has warned there would be many deaths.
In their letter, Mr Robert wrote he had checked to see if the time and place of Friday at Mar-a-Lago was still a go, and that Mr Quinn had said yes.
“President Trump stands ready, willing and able to proceed with his deposition on Friday,” Mr Trump’s attorney told the judge.
“Now that we have all traveled to West Palm Beach, and are currently sitting in the middle of a hurricane while plaintiffs’ counsel enjoys the comforts of home, plaintiffs have the gall to request that the deposition for which defendants spent considerable time and resources preparing be cancelled less than 48 hours prior to its scheduled date and time.”
Magistrate Judge Sarah Cave of the US District Court for the Southern District of New York extended the deadline of Wednesday night for Mr Quinn’s team to question Mr Trump, saying she had done so “out of concern for the safety of the parties, court reporter, videographer, and any other required attendees of the deposition”.
The new deadline for Mr Trump to be deposed is now October 31.