A grim Donald J. Trump leaned back from the defendant’s table inside a jammed 13th-floor courtroom in Miami on Tuesday, jaw set, arms crossed, his back muscles tensing visibly under his dark suit jacket.

About 20 feet away, in the second row of the visitors’ gallery, was Jack Smith, the special counsel who had put him there, alert and poker-faced. Mr. Smith looked on as three Justice Department lawyers under his supervision offered Mr. Trump a bond agreement to release him on his own recognizance, without bail, that was respectful and accommodating, but profoundly humbling.

After a 50-minute courtroom encounter unlike any other in the country’s history, Mr. Trump exited by a side door recessed in dark wood paneling, but not before allowing himself a curious peek over his shoulder at the 40 or so reporters crammed into the room.

About a minute later, Mr. Smith and his team walked to the opposite side of the room and left wordlessly. He did not look back.

The first-ever arraignment of a former president on federal charges coincided with the first public encounter between the two men, Mr. Trump and Mr. Smith, at the center of the Mar-a-Lago documents case. The two did not say a word to each other. But these most dissimilar of adversaries are locked in a legal battle with immense political and legal implications for a polarized nation.

Mr. Trump’s body language in the courtroom suggested he understood the gravity of the situation. A former president who thrives on being in control seemed uncomfortable with having so little as a defendant.

Mr. Trump, who has denounced his indictment as a witch hunt and called Mr. Smith a “thug,” did not say a word at the hearing. Nor did the magistrate judge, Jonathan Goodman, ask him a single question, as sometimes happens in criminal arraignments.

Mr. Trump has promised to have more to say later. Several of his political aides were seen outside the courthouse mixing with a small but vocal group of supporters, who were shouting their support over the chopping of a helicopter hovering above.

Inside, the hearing itself was a quiet and strikingly civil affair.

The former president, flanked by his two lawyers, Christopher M. Kise and Todd Blanche, waited patiently for at least 15 minutes for Judge Goodman to enter the courtroom. While Mr. Kise absorbed himself in paperwork, Mr. Trump and Mr. Blanche leaned in close to whisper in each other’s ears, one or twice sharing a laugh. The former president seemed for a moment or two to be at ease.

But the atmosphere changed abruptly at 2:45 p.m. A court official announced that the closed-circuit camera, which piped the hearing into a fifth-floor jury assembly room taken over for the day by the news media, had been turned on. The former president stiffened and stared directly into the camera, as if to recognize the power of the lens.

Mr. Trump, who liked to appear at the White House flanked by flags, often in front of the presidential seal, found himself on the opposite end of the visual on Tuesday. Judge Goodman sat atop a marble dais, elevated several feet above everybody else, next to an American flag in the largest, most modern hearing room in the Wilkie D. Ferguson courthouse.

It is not clear how long Mr. Trump and his co-defendant, Walt Nauta, spent in the courtroom after being booked and electronically fingerprinted by U.S. marshals in the building earlier. But the nation’s 45th president was sitting at his table, along with dozens of court and security workers, when reporters were led into the room shortly after 2:40 p.m.

Most of the substance of the hearing centered on the details of the bond agreement for Mr. Trump. Mr. Smith’s senior prosecutors waived demands for bail, or any other precondition that might be deemed as undignified or overly restrictive. They insisted that Mr. Trump not discuss the case with Mr. Nauta, who remains on the former president’s payroll as a personal aide.

Judge Goodman pressed for a tougher deal, suggesting that Mr. Trump be blocked from having any contact at all with important witnesses. His lawyers responded that the witnesses included people on Mr. Trump’s personal staff and security detail, and that it was not realistic to ask him to cut off contact with them.

The prosecution appeared willing to go along. David Harbach, one of Mr. Smith’s senior prosecutors, asked the court to let the two sides work out the details at a later date. Two earlier drafts of a bond agreement had already been discarded, but a third draft of the deal was printed and Mr. Trump signed it. “Third time’s the charm,” Judge Goodman said.

The judge seemed to be the only participant who appeared truly relaxed, perhaps because he was the only one walking away from the case. Another magistrate judge will preside over preliminary hearings before Judge Aileen M. Cannon takes over for the trial.

“The good news is it will not be me,” Judge Goodman said just before dismissing the parties.