WASHINGTON — The meeting was billed as routine, but few inside the White House expected it to be ordinary.

On that morning, Donald Trump had requested a private conversation with Barack Obama, the man who preceded him and whose presence still loomed over Mr. Trump’s political identity. Officially, the agenda concerned national priorities and continuity. Unofficially, aides understood that the encounter carried years of unresolved tension.

The two men met inside the Oval Office, a room heavy with symbolism and history. Mr. Trump, seated behind the Resolute Desk, appeared relaxed but alert, according to accounts from people familiar with the meeting. Mr. Obama entered without an entourage, greeting the president calmly and taking his seat without ceremony.

What followed was less a policy discussion than a test of demeanor.

After brief pleasantries, Mr. Trump steered the conversation toward a familiar provocation: questions about Mr. Obama’s birthplace — a conspiracy theory that had been repeatedly debunked and that Mr. Trump himself had amplified years earlier. Framing the issue as public curiosity rather than personal doubt, Mr. Trump suggested that “some people” continued to ask questions.

Those in the room immediately recognized the implication. The so-called “birther” claim had long been settled by documentary evidence, including the release of Mr. Obama’s long-form birth certificate. The theory’s persistence has been widely criticized as racially motivated and politically cynical.

Mr. Obama did not respond with visible irritation. According to those present, he paused, then replied evenly that the matter had been answered years earlier. When Mr. Trump pressed further, suggesting transparency required continued discussion, Mr. Obama compared the claim to denying the moon landing — a belief held by some, he noted, but not one that merited serious debate.

The exchange appeared to shift the balance in the room. Mr. Trump, who had seemed prepared for confrontation, instead faced silence and measured rebuttal. At one point, Mr. Obama reportedly placed a document on the desk between them: the same birth certificate that had already been made public. “The paper hasn’t changed,” he said.

The moment was quiet, but unmistakable.

As the conversation continued, Mr. Trump attempted to reassert control, contrasting what he described as his results-driven leadership with Mr. Obama’s rhetorical style. Mr. Obama responded without raising his voice. “Doing things is easy,” he said, according to one account. “Doing the right things is harder.”

The remark landed with more weight than volume. Mr. Trump’s responses grew faster, more animated. At one point, he dropped a pen, a small disruption that underscored a broader loss of rhythm. Mr. Obama, by contrast, remained composed, allowing pauses to stretch uncomfortably long.

The discussion then turned more personal.

Mr. Obama raised concerns about Mr. Trump’s public comments regarding his daughter, Ivanka Trump, who held an advisory role in the administration at the time. Because she had been granted formal influence, Mr. Obama argued, remarks made about her on television were no longer private family banter but part of the public record.

Mr. Trump bristled, calling the comments jokes and accusing Mr. Obama of distortion. Mr. Obama did not argue further. He simply repeated the words in question and allowed them to stand without commentary.

“It’s always a joke after the fact,” he said quietly, describing what he characterized as a pattern of denial and minimization.

The meeting ended abruptly. Mr. Trump stood and extended his hand, signaling a desire to move on. Mr. Obama declined the gesture, responding instead that moving forward required learning, not pretending. He then left the room without further exchange.

In the silence that followed, aides later said, the energy had shifted. The Oval Office felt less like a stage and more like a vacuum. Mr. Trump remained behind the desk, adjusting papers that did not require organizing.

Mr. Obama, for his part, never publicly discussed the meeting. In a later interview, speaking generally about leadership, he emphasized restraint over volume and clarity over confrontation. “Calm doesn’t retreat from noise,” he said. “It outlasts it.”

For those who witnessed the encounter, the contrast was instructive. Mr. Trump had entered seeking dominance through provocation. Mr. Obama responded with composure, letting facts and silence do the work that arguments often cannot.

The exchange did not produce policy shifts or headlines that day. But it offered something subtler — a study in how power is exercised, challenged and, sometimes, quietly exposed.