At a prime-time forum in Des Moines billed as a conversation about democracy and civic trust, former President Barack Obama stepped back into the political spotlight with a message that was at once measured and unmistakably pointed.

The event, held at a downtown civic center and moderated by the journalist Lauren Pierce, had been promoted as a reflection on the strains facing American institutions. The audience arrived subdued, reflecting a broader national fatigue with partisan rancor and years of escalating political confrontation.

Mr. Obama, appearing relaxed but deliberate, opened with familiar themes: the importance of norms, the fragility of democratic institutions and the responsibility of leaders to tell the truth even when it is inconvenient. He spoke in the unhurried cadence that defined much of his presidency, pausing often, as if weighing each phrase.

“What we haven’t seen before,” he said at one point, “is somebody questioning the integrity of elections and the will of the people in a way that erodes confidence not just in a candidate, but in the system itself.”

When Ms. Pierce asked how trust could be rebuilt in a country fractured by what she described as competing versions of reality, Mr. Obama did not name his successor immediately. Instead, he framed the issue more broadly.

“Truth,” he said, “isn’t supposed to depend on who’s shouting the loudest. It’s supposed to depend on facts.”

Pressed directly on whether he was referring to former President Donald J. Trump’s repeated claims of widespread voter fraud in the 2020 election, Mr. Obama nodded.

“When someone keeps telling you the sky is green,” he continued, “and you’ve got millions of people starting to believe it, at some point, for the sake of the country, you have to hold up a photograph of the blue sky.”

The metaphor drew a brief, uneasy laugh from the audience. But Mr. Obama’s tone remained sober. He described conversations with Republicans whom he said he respected — individuals, he implied, who privately acknowledged the absence of evidence supporting claims of systemic fraud even as public rhetoric continued.

Then came the moment that shifted the evening’s tone. Mr. Obama said he had documentation to illustrate how doubts about the election were, in his words, “manufactured.” Behind him, a large screen displayed what were described as authenticated communications among senior political figures discussing strategies to sustain public skepticism about the results, despite internal assessments showing no substantive irregularities.

The presentation, which included excerpts of emails and internal memos, appeared designed to move the debate from abstract argument to documented evidence. Mr. Obama did not linger on each slide, but the implication was clear: the persistence of election-fraud narratives, he suggested, was not merely a misunderstanding but a calculated political strategy.

The audience watched in near silence. For some, the moment felt like a rare breach of the informal code that former presidents traditionally observe — a reluctance to criticize successors or successors’ campaigns in direct terms. Mr. Obama has generally adhered to that norm, intervening only sparingly in partisan disputes since leaving office.

Within hours, Mr. Trump responded forcefully on social media, denouncing the presentation as a “witch hunt” and accusing Mr. Obama of spreading falsehoods. By the following morning, he appeared before reporters in an unscheduled appearance, visibly animated.

“Did you see what he did?” Mr. Trump asked, referring to Mr. Obama. He dismissed the documents as fabricated and described the episode as part of a broader conspiracy against him.

When a reporter attempted to ask about the materials shown during the forum, Mr. Trump cut in, calling them “fake” and “deep state forgeries.” He did not engage in a detailed rebuttal of the documents’ contents.

The exchange underscored a widening rift not just between the two men, but between competing narratives about the 2020 election. Courts across the country, including those with judges appointed by Mr. Trump, have repeatedly rejected claims of widespread fraud. Yet polls show that a significant portion of Republican voters continue to harbor doubts about the election’s legitimacy.

Political historians noted that direct confrontations between former presidents are rare. “There’s a longstanding tradition of restraint,” said Julian Zelizer, a professor of history at Princeton University. “Former presidents tend to avoid escalating conflicts with their successors, in part to protect the institution itself.”

Mr. Obama’s decision to present documentary evidence in a public forum marks a departure from that pattern. Supporters argue that extraordinary circumstances — including threats and harassment faced by election officials in the aftermath of 2020 — justify a more assertive response. Critics counter that such interventions risk deepening polarization.

What was striking about the Des Moines event was not the volume of the rhetoric, but its contrast. Mr. Obama’s delivery was calm, almost clinical. Mr. Trump’s reaction was animated and combative. The juxtaposition reinforced long-standing differences in style that have defined the political rivalry between the two men.

Whether the episode will shift public opinion is uncertain. In an era of entrenched partisan identities, even documentary evidence can be filtered through ideological lenses. But the forum illustrated a broader question facing American democracy: how to reconcile a commitment to open debate with the need for shared facts.

For one evening in Iowa, that question moved from abstraction to spectacle. A former president held up what he called proof. A successor called it fiction. Between those claims lies the ongoing struggle over who gets to define reality in American politics.