Nearly two weeks after he was released by a Manhattan judge on a $250 million bond and ordered to stay with his parents in Palo Alto, Calif., Sam Bankman-Fried, the disgraced cryptocurrency executive, returned to New York and pleaded not guilty on Tuesday to charges that he engaged in widespread fraud, paving the way for a possible trial.

Mr. Bankman-Fried, 30, appeared in Federal District Court in Manhattan, where he faces charges stemming from the implosion of FTX, the cryptocurrency exchange he founded and led. Its collapse resulted in billions of dollars in customer losses.

Mr. Bankman-Fried could ultimately change his mind and plead guilty to at least some of the charges. But his initial response tees up a potentially titanic court fight. The judge, Lewis A. Kaplan, set a tentative trial date of Oct. 2.

Mr. Bankman-Fried did not speak during the hearing, and the not-guilty plea was entered on his behalf by one of his lawyers, Mark Cohen. Throughout the court session, which lasted about half an hour, Mr. Bankman-Fried, wearing a dark jacket and tie, sat between his two lawyers, occasionally scribbling notes and leaning over to consult with one of them.

The hearing was the latest step in an unusually fast-moving investigation. Mr. Bankman-Fried was arrested on Dec. 12 at his luxury apartment in the Bahamas, where FTX was based until it filed for bankruptcy in November.

An eight-count indictment charged him with a multiyear scheme that defrauded customers and lenders, and with violations of federal campaign finance laws. Prosecutors have accused him of misappropriating billions to buy real estate in the Bahamas, trade digital currencies, invest in other crypto companies and make tens of millions of dollars in campaign donations.

After Mr. Bankman-Fried was extradited to the United States in late December, he appeared in court and was granted bail under highly restrictive conditions, including the rule that he stay confined to his parents’ home in Palo Alto.

At the hearing on Tuesday, prosecutors requested a new bail condition prohibiting Mr. Bankman-Fried from transferring any funds controlled by FTX or Alameda Research, a crypto hedge fund that he also founded.

The request came in response to claims that circulated last week that Mr. Bankman-Fried was moving cryptocurrencies from digital accounts controlled by Alameda.

Mr. Bankman-Fried denied the reports on Twitter. In court, Danielle Sassoon, an assistant U.S. attorney, said that prosecutors had no evidence that Mr. Bankman-Fried had moved the funds himself, but that they had reason to distrust his public statements.

“We don’t put full stock in that simply because our investigation has revealed that he has tweeted knowing false statements before,” she said.

Judge Kaplan authorized the bail condition.

The judge also took up a request by Mr. Bankman-Fried’s lawyers to keep secret the names of two people who, along with the FTX founder’s parents, had agreed to sign bonds to help assure his appearance in court.

In a letter filed with the judge on Tuesday morning, the lawyers noted that Mr. Bankman-Fried’s parents — the Stanford Law School professors Joe Bankman and Barbara Fried — had in recent weeks become “the target of intense media scrutiny, harassment and threats.”

Among other things, the lawyers wrote, the parents had received “a steady stream of threatening correspondence, including communications expressing a desire that they suffer physical harm.”

Judge Kaplan said he would grant the request, but left open the possibility that he would revisit the issue if there was opposition.

“I anticipate the possibility that members of the media or others may wish to contest the sealing of that information,” Judge Kaplan said.

Mr. Bankman-Fried faces an uphill battle fighting the charges by U.S. prosecutors. As he was flown back to the United States in December, prosecutors announced that two former executives of his crypto-trading empire had pleaded guilty to federal fraud charges and were cooperating in the investigation.

They were Caroline Ellison, 28, who was the chief executive of Alameda, as well as Mr. Bankman-Fried’s onetime girlfriend; and Zixiao “Gary” Wang, 29, a founder of FTX.

At the hearing on Tuesday, Ms. Sassoon said the government had also amassed hundreds of thousands of documents, including material turned over by banks, employees, political campaigns, internet service providers and the new leadership of FTX.

When Mr. Bankman-Fried was released on bond last month, a magistrate judge approved a bail package that required him to be confined to his parents’ home and to wear an electronic monitoring bracelet. Since then, he has been relatively quiet; usually a prolific tweeter, he has posted only twice in recent days, and only to rebut the claims that he was secretly moving crypto funds.

But he has received at least two visitors at his parents’ home. One of them, the author Michael Lewis, is writing a book about Mr. Bankman-Fried, and in the months before FTX’s collapse, he met with him in the Bahamas to conduct interviews. Mr. Lewis’s visit was first reported by The New York Post and was confirmed by The New York Times.

Mr. Bankman-Fried also met with Tiffany Fong, who runs a crypto-themed YouTube page. She shared an account of the meeting on Substack, writing that Mr. Bankman-Fried seemed “a bit more trepidatious about upsetting his lawyers during this chat than he has in the past.” In the weeks before Mr. Bankman-Fried was arrested, Ms. Fong conducted two phone interviews with the FTX founder and posted recordings on YouTube.

The terms of Mr. Bankman-Fried’s bail are silent on whether he is allowed to receive visitors to his home and post on social media. On Friday, he posted the two messages on Twitter, disputing claims that after his release he transferred cryptocurrencies from digital wallets associated with Alameda.

Those claims started circulating after crypto experts noticed that digital accounts associated with Alameda were transferring funds. The movement of the money was visible because cryptocurrency transactions are recorded on a public ledger that anyone can access and analyze.

In court, Ms. Sassoon said that prosecutors were investigating the transfers. “While we don’t know whether it was the defendant who made these transfers, he did at one point have access to these wallets,” she said.

Mr. Cohen denied that Mr. Bankman-Fried had made the transfers.

Ms. Sassoon also alluded to a brewing jurisdictional battle between FTX’s new leadership, which is overseeing the bankruptcy process in the United States, and the government of the Bahamas. She said that Mr. Bankman-Fried had helped foreign regulators obtain FTX assets, and that he had expressed an intention to “stall” the U.S. bankruptcy process.

Since he authorized FTX to file for bankruptcy on Nov. 11, Mr. Bankman-Fried has said repeatedly that he regretted the decision. While Ms. Sassoon was speaking, the FTX founder looked agitated, shaking his head and scribbling a note to his lawyer. Mr. Cohen told the judge that the transfer to regulators that Ms. Sassoon was describing had been ordered by a court in the Bahamas.

Judge Kaplan was assigned a week ago to preside in Mr. Bankman-Fried’s case after the original judge, Ronnie Abrams, said she was recusing herself because the law firm Davis Polk & Wardwell, where her husband is a partner, had done work for FTX in 2021. Although her husband was not involved in that representation, she said, she was withdrawing to “avoid any possible conflict, or the appearance of one.”

Prosecutors have vowed to continue investigating, and it’s possible more executives in Mr. Bankman-Fried’s orbit could be charged. On Tuesday, Damian Williams, the U.S. attorney for the Southern District of New York, announced the creation of a special FTX task force of prosecutors drawn from his office’s units that investigate securities fraud; public corruption; and money laundering and transnational crimes. The task force will be led by Andrea Griswold, the chief counsel to the U.S. attorney.

Liset Cruz contributed reporting.