Mr. Sheridan came close to an apology, telling Judge Snow: “I’m ashamed of the things I said. I mischaracterized your order, there is no doubt about that. I had gotten some facts incorrect.”

Tim Casey, a lawyer for Mr. Arpaio, reminded the judge that emotions were still raw at the time the video was recorded, barely two months after a detention officer at the sheriff’s department was shot to death in his front yard in southwest Phoenix. He also said that there was “an adjustment process” whenever change was imposed “by outside forces.”

Judge Snow leaned closer to the microphone, locked his gaze on Mr. Casey and told him, “It isn’t a new order.” The facts it laid out had been raised as far back as 2011, when he issued a preliminary injunction in the case, he said.

Sheriff Arpaio did not speak in court; he sat just behind the defendants’ table, his chin propped on his right hand as he faced Judge Snow. After the hearing, outside the courthouse, he struck a tone of defiance, telling reporters: “We’ll be appealing this case anyway. Stay tuned.”

Throughout the case, which has gone on for years, Mr. Arpaio has vigorously denied the allegations. And although he remains a polarizing figure, his supporters have stuck by him: Donations to his campaign fund have continued to pour in, from inside and outside Arizona, and have already surpassed $3 million for the 2016 election, when he plans to seek a seventh term as sheriff. Although he has floated the idea of running for governor of Arizona this year, to replace Jan Brewer, a Republican, as she leaves office, even some of his closest advisers doubt he will do so.

The case before Judge Snow is a class-action lawsuit on behalf of Latinos who have been or will be stopped by Mr. Arpaio’s deputies in Maricopa County. But Mr. Arpaio and the Maricopa County Sheriff’s Office still face another lawsuit, filed by the Justice Department, claiming civil rights violations, based on, among other things, a longstanding pattern of discrimination against Latinos.

To Judge Snow, the hearing was an opportunity to put the alleged violations and mischaracterizations of his orders on the record. He made clear that if there were any further violations, he would not hesitate to use his authority to impose further sanctions on the sheriff’s office, like hiring more monitors to make sure the deputies were no longer discriminating against Latinos.

To underscore his points, Judge Snow asked that the lawyers on both sides of the case prepare a summary of his order and that Mr. Arpaio and his deputies use it as a training tool, ideally to make sure none of it was misinterpreted. He also asked both sides to sign a letter attesting to the intentions of the order, which Mr. Arpaio’s lawyers said they would have to discuss before accepting.