Attorneys for billionaire sex offender Jeffrey Epstein asked a federal judge Thursday to allow him to post bail and await his upcoming child sex trafficking trial at his posh Upper East Side townhouse.

Mr. Epstein’s attorneys offered to put up his $77 million New York home and his private jet as collateral. In exchange, they asked for his release on house arrest and GPS monitoring.

Saying their client intends to challenge the charges in “a lawful, professional principled manner,” defense attorneys asked the judge to put aside the media and political firestorm the case has sparked.

“No matter how much rhetoric and hyperbole the government and media pile on a presumptively innocent citizen compelling legal issues stand between Mr. Epstein and any possible conviction on the allegations of conduct,” wrote defense attorney Reid Weingarten.

Mr. Epstein has pleaded not guilty to the charges of sex trafficking and conspiracy.

Federal prosecutors said earlier this week they would oppose bail, portraying 66-year-old billionaire as a man of “infinite means” who posed a substantial flight risk.

“The is no combination of conditions that would reasonably assure his continued appearance in this case or protect the safety of the community were he to be released,” Assistant U.S. Attorney Alex Rossmiller said at Mr. Epstein’s arraignment Monday.

Defense attorneys claimed that Mr. Epstein has “an exemplary 10-year history” of complying with reporting as a sex offender, and said that proved he’ll comply with any bail restrictions he’s given now.

But a New York Post report Thursday claimed that Mr. Epstein skipped his court-ordered check-ins with law enforcement for eight years.

As a Level 3 registered sex offender, Mr. Epstein was required to report to the New York Police Department every 90 days and confirm his residency. Mr. Epstein, though, said he didn’t need to report because his primary residence is in the U.S. Virgin Islands, according to The Post.

New York Mayor Bill de Blasio fumed at the report, calling Mr. Epstein “a danger to society.”

“Something’s very broken,” the mayor said during an interview on MSNBC. “He gamed the system and used a legal loophole to get away with it. It’s ridiculous.”

The Epstein case has roiled national politics, with much of the focus falling on Labor Secretary Alex Acosta, who as a federal prosecutor in Miami oversaw a nonprosecution deal that let Mr. Epstein plead guilty to a state charge of soliciting prostitution. He served a 13-month sentence and was required to register as a sex offender.

Mr. Acosta held a press conference Wednesday defending the plea deal, saying he intervened because state prosecutors were pursuing a charge that would have let Mr. Epstein walk free with no jail time. The Palm Beach state attorney at that time, Barry Krischer, has accused the labor secretary of trying to rewrite history.

Democrats said Mr. Acosta has more explaining to do and should face questions from lawmakers.

“Standing up in front of a camera and having a decent press conference has nothing to do with his dereliction of duty,” said Rep. Val Demmings, Florida Democrat and a former police chief. “His press conference did not move me in his favor at all.”

Rep. William Clay, Missouri Democrat, said the committee has not heard back from Mr. Acosta but he does not expect the labor secretary to show.

“Most of the administration has been dodging Congress,” he told The Washington Times.

Rep. Jim Jordan of Ohio, the committee’s ranking Republican, slammed the request for Mr. Acosta to testify.

“It’s part of a pattern,” he said. “It is a nonstop effort to go after the president. Maybe they should send a little more time on helping us address problems at the border and other concerns Americans have.”

But Rep. Mark Meadows, North Carolina Republican, encouraged Mr. Acosta to appear and face lawmakers’ questions.

“It was a good press conference, but I think coming before Oversight and being able to answer questions from both sides of the aisle should be appropriate,” he said.

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