FTX’s new chief executive, John J. Ray III, said he is looking into the possibility of reviving the bankrupt crypto exchange as he works to return money to the failed company’s customers and creditors.   

In his first interview since taking over FTX in November, Mr. Ray said that he has set up a task force to explore restarting FTX.com, the company’s main international exchange. Although top FTX executives have been accused of criminal misconduct, some customers have praised its technology and suggested that there would be value in rebooting the platform, he said.

“Everything is on the table,” Mr. Ray said. “If there is a path forward on that, then we will not only explore that, we’ll do it.”

FTX’s bankruptcy filing marked the largest of several failures of cryptocurrency platforms last year that froze millions of users’ access to their accounts. FTX, Celsius Network LLC, Voyager Digital Ltd. and BlockFi Inc. have used the chapter 11 process to explore restarting their businesses and selling their platforms to stronger rivals. Another option is to simply close up shop and return crypto holdings to customers as quickly as possible.

Mr. Ray said he would look into whether reviving FTX’s international exchange would recover more value for the company’s customers than his team could get from simply liquidating assets or selling the platform.

“There are stakeholders we’re working with who’ve identified what they see is a viable business,” he said.

Even if a reboot gets traction, the outlook for FTX’s customers remains highly uncertain. On Tuesday, FTX identified “substantial shortfalls” of digital assets at its U.S. and international exchanges relative to how much its customers are owed.

Mr. Ray’s job now is to identify any remaining pockets of value that could help plug that shortfall, the size of which FTX hasn’t disclosed. He is a veteran of restructuring troubled companies, most famously Enron Corp., where he helped return billions of dollars to the troubled energy trader’s creditors. After inheriting the top job at FTX, whose co-founders have been accused of misusing customer funds, Mr. Ray has worked to locate and secure assets belonging to its customers, who have been locked out of their accounts. 

When he took over 69 days ago, Mr. Ray said he was given no indication of where FTX staff kept its customers’ cryptocurrency and cash. He and his skeleton staff discovered there was no centralized register that identified where the company stored its funds.

Mr. Ray said initially he got help from FTX co-founder Gary Wang and the former CEO of its affiliated trading firm Alameda Research, Caroline Ellison, in trying to track the companies’ funds. Mr. Wang and Ms. Ellison later pleaded guilty to criminal charges related to FTX.

Sam Bankman-Fried outside Manhattan federal court earlier this month. John J. Ray III said that some of the comments from FTX’s former CEO have been unhelpful and self-serving.

Photo: ed jones/Agence France-Presse/Getty Images

Mr. Ray has clashed with FTX’s former CEO and co-founder Sam Bankman-Fried, who faces federal fraud and other criminal charges and has pleaded not guilty. Mr. Bankman-Fried has said it was a mistake for FTX to file for chapter 11 and criticized Mr. Ray’s handling of the company.

Mr. Ray said in the interview that Mr. Bankman-Fried’s comments were unhelpful and self-serving.

“We don’t need to be dialoguing with him,” Mr. Ray said. “He hasn’t told us anything that I don’t already know.”

Mr. Bankman-Fried responded in a text message: “This is a shocking and damning comment from someone pretending to care about customers.”

Over the past two months, Mr. Ray radically overhauled FTX’s structure, which had effectively no corporate governance to speak of, and cut dozens of employees, he said. His forensic teams are still combing through more than 30 terabytes of FTX’s data to find any information that could lead them to more money. The firm has discovered new wallets in the past week alone, he said. 

FTX disclosed in bankruptcy court last week that it had found $5 billion in liquid assets and a $4.6 billion investment portfolio. Customers viewed that as positive, though it isn’t clear how much of that book value can be realized from the stakes that FTX and Alameda bought in crypto startups and other private ventures.

Mr. Ray has engaged investment bankers to sell some of FTX’s subsidiaries and venture investments. FTX, Alameda and other entities controlled by Mr. Bankman-Fried put more than $5 billion into more than 150 startups, as well as venture firms like Sequoia Capital, The Wall Street Journal has reported.

“They went on a spending spree” unlike any he had seen in his multidecade career cleaning up companies, Mr. Ray said.

Often, Mr. Ray said, there was no record or proof of transaction behind many of the multimillion-dollar deals done by Mr. Bankman-Fried during boom times for the crypto industry, when FTX became one of the world’s top crypto exchanges.

“Sometimes there were no purchase agreements, or the agreements weren’t signed,” he said. Mr. Ray added that the bankers on his team have had to call companies in which FTX invested to discover how much they paid for the stake and what the underlying business is.

Mr. Bankman-Fried, whose bail conditions have kept him largely confined to his parents’ house in California, continues to criticize how FTX is being managed through chapter 11. On Tuesday, he disputed Mr. Ray’s claims of a shortfall on FTX’s U.S. exchange. Writing on a newly created blog, Mr. Bankman-Fried posted purported tables of estimated FTX bank balances that displayed a surplus of several hundreds of millions of dollars to cover U.S. customer claims.

Mr. Ray said that Mr. Bankman-Fried’s calculations appear to include around $250 million of cash that sits at LedgerX, the regulated U.S. crypto derivatives business that FTX purchased in 2021. The problem, Mr. Ray said, was that LedgerX itself was bought with funds from Alameda Research, which improperly diverted funds from FTX’s international exchange.

Effectively, Mr. Bankman-Fried’s proposed balance sheet would imply covering losses at the U.S. exchange through money that belongs to other customers, Mr. Ray said. 

“This is the problem,” Mr. Ray said. “He thinks everything is one big honey pot.”

Mr. Bankman-Fried responded in a text message: “Mr. Ray continues to make false statements based on nonexistent calculations. If Mr. Ray had bothered to think carefully about FTX US, he would likely have realized both that his interpretation is wholly inconsistent with bankruptcy law, and also that even if one were to subtract $250m from my balance sheet, FTX US would *still* have been solvent. Rather, Mr. Ray sees everything as one big honey pot—one he wants to keep.”

Mr. Ray added that Mr. Bankman-Fried’s explanations about what went wrong at FTX under his leadership have often been misleading and confusing to customers.

“That’s unfortunate because people are continuing to be victims right now. They are victims of misinformation,” Mr. Ray said. “It’s harmful.”

Mr. Ray also defended himself against critics who allege he is more motivated by generating fees for himself than salvaging the FTX estate. Court filings show he makes $1,300 an hour. That cost—and the cost of the myriad lawyers, accountants and other experts working on the chapter 11 team—comes out of funds that would otherwise be used to repay FTX customers and creditors.

Mr. Ray said that the high levels of criminal activity surrounding FTX make it difficult to trust some existing employees, leaving him with little option but to retain seasoned professionals with expertise in dealing with criminal corporate activity, who typically come with a steep price tag.

“Crime is very expensive. It does a lot of damage to people,” he said. “And one of the damages is that people like me have to come in and fix it.”

Write to Alexander Saeedy at alexander.saeedy@wsj.com and Alexander Osipovich at alexo@wsj.com