Earlier today Judge Lewis Kaplan announced he would unseal the deposition Trump made in October.
But he reversed that decision hours later at the request of his lawyers.
Journalist and author E. Jean Carroll alleged Trump raped her in the dressing room of a New York department store in the mid-1990s.
When Trump responded by accusing her of lying, she sued him for defamation.
On December 19 last year, Kaplan notified Trump that he would have to explain why his deposition should be redacted within three days.
"Defendant did not do so and has made no effort to justify the continued sealing of his deposition," Kaplan wrote in an order earlier today.
He ordered all previously redacted portions of the deposition should be placed on the unrestricted public record.
But at the request of Trump's lawyers, Kaplan held off his order.
They now have three days to file a letter explaining why the deposition should be redacted.
Trump was questioned by the lawyers of Carroll at his country club Mar-a-Lago in October over the course of five and a half hours.
That deposition was videotaped.
A redacted transcript of his deposition has already been released, consisting of 28 pages of blacked-out text.
But much of Carroll's deposition recorded a few days earlier has already been released.
Carroll was quizzed by Trump's lawyer about her dating life and her sex drive.
"Have you ever questioned if what happened in that dressing room was rape?" Trump's lawyer Alina Habba asked.
Carroll replied: "I question whether he thought it was rape. I never questioned what I thought."
Carroll first publicly claimed Trump had raped her in 2019.
The then-president responded by saying Carroll was "not my type" and denied they had ever met.
But photos exist of the two speaking to one another.
"It is a hoax and a lie, just like all the other hoaxes that have been played on me for the past seven years," Trump said.
Trump can not be charged with raping Carroll because the statute of limitation had passed.
At the time, alleged victims had only five years to come forward with accusations for criminal charges to be filed.
Potential criminal charges in Georgia
Meanwhile, a grand jury investigation of potential election interference by Trump has wrapped up in Georgia.
The Fulton County grand jury has been considering evidence against Trump since May last year.
A report has now been delivered to a judge, who will determine if it will be made public later this month.
Whether Trump or any of his acolytes are charged with election interference in Georgia depends in large part on recommendations made in the as-yet-unseen report.
Central to the investigation is a phone call made by Trump soon after the 2020 election to Georgia's top elections official, Secretary of State Brad Raffensberger.
The conversation was recorded by Raffensberger in his office in Fulton County, in the state capital of Atlanta.
"The people of Georgia are angry, the people of the country are angry. And there's nothing wrong with saying that, you know, um, that you've recalculated," Trump said.
"So look, all I want to do is this, I just want to find 11,780 votes, which is one more than we have. Because we won the state."
If found guilty of election fraud, Trump could face up to ten years in prison.
The state was won by Joe Biden in the 2020 election, albeit by a narrow margin.