Prosecutors also requested the judge prohibit Mr. Bankman-Fried from communicating through encrypted messaging applications like Slack and Signal, saying that when he headed FTX he directed employees of the company and his crypto-investment firm Alameda Research to set their communications on these platforms to auto-delete after 30 days. That policy has impeded the government’s investigation, prosecutors said.

“Potential witnesses have described relevant and incriminating conversations with the defendant that took place on Slack and Signal that have already been autodeleted because of settings implemented at the defendant’s direction,” prosecutors said in the filing.

Lawyers for Mr. Bankman-Fried in a letter to the judge said the government was mischaracterizing innocuous conduct by their client in “an apparent effort to portray our client in the worst possible light.” They said the government’s request was overbroad and unnecessary, proposing instead that Mr. Bankman-Fried be prohibited from contacting certain limited witnesses, not all of FTX’s current and former employees.

FTX’s U.S. general counsel, Ryne Miller, couldn’t immediately be reached.

The Manhattan U.S. attorney’s office charged Mr. Bankman-Fried last month with stealing billions of dollars from FTX customers while misleading lenders and investors. He pleaded not guilty and is currently under court-ordered confinement in his parents’ Palo Alto, Calif., home while he awaits trial.

Mr. Bankman-Fried sent a Jan. 15 Signal message to the general counsel in which prosecutors allege he said he “would really love to reconnect and see if there’s a way for us to have a constructive relationship, use each other as resources when possible, or at least vet things with each other.”

Prosecutors didn’t identify the other employees that Mr. Bankman-Fried has allegedly tried to contact but called the communications to the general counsel and others troubling.

“Were the defendant to ‘vet’ his version of relevant events with potential witnesses, that might have the effect of discouraging witnesses from testifying in a manner contrary to the defendant’s narrative,” the Justice Department said in the filing.

Mr. Bankman-Fried’s lawyers said the message to Mr. Miller was more reasonably read as an attempt by Mr. Bankman-Fried to offer his assistance to FTX, not a “sinister attempt” to influence testimony at trial.

Write to James Fanelli at james.fanelli@wsj.com