DAVOS, Switzerland — The World Economic Forum is accustomed to controversy. It has hosted autocrats and activists, financiers and firebrands. What it is less accustomed to is uncertainty about whether a speaker is describing policy, improvising grievance, or simply losing track of his own assertions. That uncertainty hovered over President Donald Trump’s appearance this week, leaving allies unsettled and raising new questions about America’s reliability on the world stage.

Mr. Trump’s speech to the forum was sprawling and combative. Over more than an hour, he assailed NATO partners, revived his long-standing fixation on acquiring Greenland, and suggested that extraordinary concentration of power could be justified in moments of crisis. At one point, he repeatedly referred to Iceland while discussing Greenland, an error that quickly became emblematic of a broader concern: not simply what the president believes, but how firmly those beliefs are anchored to fact.

In isolation, any single misstatement might have been dismissed as rhetorical excess. Taken together, diplomats said, the remarks reinforced a sense that Washington’s position could shift from sentence to sentence. “The issue isn’t embarrassment,” said a senior European official, speaking on the condition of anonymity. “It’s unpredictability.”

The reaction was swift, if understated. While no formal sanction or exclusion was announced by the World Economic Forum, several participants described an atmosphere that cooled noticeably around the American delegation. Invitations to private sessions were scarce. Conversations that might once have included U.S. officials moved elsewhere. By the forum’s closing day, attention had shifted decisively toward leaders offering steadier messages.

That contrast was embodied by Mark Carney, whose address emphasized cooperation, multilateralism and democratic resilience. Mr. Carney avoided direct references to Mr. Trump, but the juxtaposition was unmistakable. Where the American president portrayed alliances as transactional burdens, the Canadian leader framed them as strategic assets. The applause, attendees said, reflected relief as much as agreement.

The Greenland dispute sharpened those divisions. Mr. Trump has floated the idea of U.S. control over the territory for years, arguing that it is vital to American security. In Davos, he again suggested that Washington could secure new arrangements there, while adding that he would prefer not to use force — language that analysts compared to a threat followed by reassurance. Officials in Denmark and Greenland promptly reiterated that no talks on sovereignty were under way and that territorial integrity was nonnegotiable.

NATO officials, too, distanced themselves. Representatives of NATO said they had not discussed any new security framework involving Greenland, contradicting claims circulating after the speech. The episode fed a lingering anxiety in Brussels: that allies might learn of major U.S. initiatives only after they appear in public remarks.

The unease extended beyond Europe. Volodymyr Zelenskyy, speaking in Davos, urged democratic nations to present a united front against authoritarian pressure. Though his focus was the war in Ukraine, many in the audience interpreted his remarks as a broader warning about hesitation and mixed signals — particularly from Washington.

The White House dismissed suggestions that the president had been sidelined. A spokesperson said reports of exclusion were exaggerated and argued that Mr. Trump’s blunt style reflected a mandate from voters skeptical of global institutions. Supporters contended that Davos elites were reacting defensively to a leader unwilling to conform to their consensus.

Markets told a more complicated story. Financial volatility earlier in the week eased only after it became clear that some of the president’s more provocative statements were being walked back or reframed. Investors, analysts said, were less concerned with ideology than with the possibility of abrupt policy shifts announced without coordination.

Behind the scenes, officials acknowledged that trust — once strained — is difficult to restore. Even if Washington ultimately retreats from its most controversial positions, the memory of the threats lingers. “You can’t unring that bell,” said a former U.S. diplomat. “Partners plan for what might happen, not just what is promised.”

The Davos episode also revived debate about the future of American leadership. For decades, the presence of a U.S. president at the forum signaled continuity, even amid disagreement. This year, influence appeared to flow toward those offering predictability rather than power. The shift was subtle but significant: fewer headlines about expulsions or bans, more about absence and avoidance.

Forum officials declined to comment on whether Mr. Trump would be invited again, noting that invitations are reassessed annually. Privately, several participants said the question was less about formal access than about relevance. “If leaders don’t believe what they hear, they stop listening,” said one European executive.

As the Alpine resort emptied and delegations departed, no single moment defined the week. There was no dramatic walkout, no official rebuke. Instead, there was something quieter: a sense that the United States, once the gravitational center of Davos, had drifted to the periphery of the conversation.

Whether that drift becomes permanent will depend on choices made far from Switzerland. For now, the lesson many took from Davos was not that President Trump had been barred from the global stage, but that the stage itself is changing — and that credibility, once questioned, is far harder to reclaim than attention.