President Trump had nothing on his public schedule for three days last week. He is often sporting a large, purple bruise on his right hand, which he sometimes slathers with makeup. His ankles are swollen. He is the oldest person to be elected president.

For a swath of hyper-online Americans over the long Labor Day weekend, all of this was explanation enough: The president was either dead or about to be.

Mr. Trump’s critics have speculated about his health for as long as he has been in national politics. And for his part, he has long declined to explain when and why he has sought out medical care, whether he was suffering from Covid or undergoing routine procedures. But there had never been a conspiracy wave as feverish as this one.

On TikTok, influencers with legions of followers surmised that the White House was publishing old photos, suggesting that the president was being hidden from view. Reddit threads, one after another, were ablaze with commentary. On X, posts shared by anonymous critics disseminating dubious reports picked up thousands of interactions and shares.

There was so much conversation around the president’s absence that Mr. Trump was asked to weigh in on Tuesday, at his first official public appearance in a week. When asked by a reporter how he first learned that he was dead, Mr. Trump said that he was not aware of the rumors that he had died. Then he started speaking about those rumors at length, saying he had done media appearances, gone golfing at his Virginia club and posted prolifically on his social media site.

“I did numerous shows, and also did a number of Truths,” Mr. Trump said during an appearance in the Oval Office, referring to his social media site, where he posted over 90 times between Saturday and Monday. “I think, pretty poignant Truths. I was very active over the weekend.”

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