In Washington on Tuesday evening, a much-anticipated “national leadership forum” featuring President Donald Trump and former President Barack Obama unfolded less as a policy discussion than as a vivid study in contrast — temperament versus provocation, volume versus restraint.

The event, held in a grand hall blocks from the White House, was billed as a conversation about unity and the challenges facing the country. Yet from the outset, the atmosphere suggested something more combustible. Reporters crowded the aisles. Camera flashes punctuated the dim light. Two lecterns stood at the front of the room, separated by a long table set with microphones and water glasses — a physical reminder of the political distance between the men who would occupy them.

Mr. Trump entered first, offering a brief wave before taking his seat. When Mr. Obama followed minutes later, the mood shifted perceptibly. The two had not shared a public stage since Mr. Trump’s return to office, and the rarity of the moment hung heavily in the room.

After a brief introduction from the moderator, Mr. Trump began with what sounded at first like a conventional critique of his predecessor’s record. He questioned the economic gains of the Obama years and argued that his own administration had delivered more tangible results. But the tone sharpened quickly.

“For eight long years, America didn’t have results,” Mr. Trump said, characterizing Mr. Obama’s presidency as one defined more by rhetoric than achievement. He accused the former president of leaving behind economic weakness and political division, and he framed his own tenure as an effort to “clean up the mess.”

The remarks grew increasingly personal, culminating in a series of blunt characterizations that drew audible reactions from the audience. Mr. Obama, seated across the table, remained still, his hands folded, his expression composed.

When the moderator turned to him for a response, Mr. Obama did not immediately speak. The pause, stretching several seconds, seemed to recalibrate the room.

“When people get that loud,” he began evenly, “it usually means they’re trying to cover up something quiet — the truth.”

Rather than rebutting each allegation, Mr. Obama addressed what he described as a broader pattern in political discourse. Leadership, he said, was not about assigning blame but about taking responsibility. “When leaders spend their time blaming others,” he added, “they’re not leading. They’re just talking.”

The audience, which had responded to Mr. Trump’s comments with a mixture of applause and unease, listened in near silence. Mr. Obama acknowledged that his presidency had not been without mistakes, but he emphasized that decisions had been made with working families and small businesses in mind. The test of leadership, he suggested, lay less in volume than in empathy and accountability.

“Leadership isn’t about pointing backward,” he said. “It’s about looking forward.”

For several minutes, the exchange appeared to settle into a familiar rhythm: accusation followed by reflection, provocation followed by measured reply. But tensions rose again when Mr. Trump returned to the microphone, dismissing Mr. Obama’s remarks as “smooth talk” and reiterating claims about economic decline and political division.

The confrontation escalated as both men alluded to past controversies and grievances. At one point, Mr. Obama referenced remarks Mr. Trump had made years earlier about his daughter — comments that had drawn scrutiny at the time. The mention prompted visible irritation from Mr. Trump, who called the reference inappropriate and warned that personal lines were being crossed.

“You can attack me all you want,” Mr. Obama replied calmly. “But real strength doesn’t need volume. It needs truth.”

The exchange, now unmistakably personal, seemed to test the boundaries of what the forum’s organizers had envisioned. The moderator attempted to interject, but the two men continued, each framing the other as emblematic of deeper national problems — one of excessive ego and anger, the other of elitism and detachment.

Then, abruptly, Mr. Trump stood. Calling the discussion “a joke,” he declared that he would not “sit here listening to another word” and left the stage, trailed by aides and security personnel. His empty chair remained under the bright lights as the audience murmured in surprise.

Mr. Obama stayed seated. After a moment, he leaned toward the microphone.

“That’s what happens when anger becomes stronger than truth,” he said quietly. He added that the nation’s challenges would not disappear because someone chose to walk away from difficult conversations.

A subdued wave of applause followed, gradually building as audience members rose to their feet. The applause was not thunderous but sustained, reflecting perhaps more relief than triumph.

The evening offered no policy breakthroughs and little in the way of new arguments. Instead, it underscored the enduring divide between two political figures whose styles could hardly be more different. For Mr. Trump, confrontation remains a central tool, a way to dominate a room and energize supporters. For Mr. Obama, composure and rhetorical restraint serve as counterweights.

Whether the exchange will shift public opinion is uncertain. But as images of the vacant chair and the former president standing alone circulated online, the symbolism proved difficult to ignore.

In a political era defined by spectacle, Tuesday’s forum became another chapter in an ongoing contest over what leadership looks like — and which style resonates most in a country still wrestling with its divisions.