Four minutes after the first report of a shooting at a rally for Donald J. Trump on Saturday, an anonymous account on X posted, “Joe Biden’s antifa shot President Trump.”

Within half an hour, another account on X with links to the QAnon conspiracy theory claimed without proof that the attack against Mr. Trump had most likely been ordered by the Central Intelligence Agency. Shortly after that, the far-right activist Laura Loomer posted on X about some recent remarks that President Biden made about Mr. Trump and then wrote, “They tried to kill Trump.” She did not provide evidence.

An hour later, with official details of the assassination attempt still scant, the narrative that President Biden and his allies had engineered the attack on Mr. Trump was being amplified by Republican lawmakers, Russian sympathizers and even a Brazilian political scion. By the time 24 hours had elapsed, posts about the unverified claim had been viewed and shared millions of times.

The idea that President Biden was behind the shooting of Mr. Trump was perhaps the most dominant conspiracy theory to emerge after the attack in Butler, Pa., on Saturday. The unproven conjecture surfaced almost instantly, hardened into a narrative and then catapulted between platforms large and small, even as information about the incident was limited. It was a striking example of the speed, scale and stickiness of rumors on social media, which often calcify into accepted truth far more efficiently than efforts to debunk or pleas for restraint.

That the subject this time was Mr. Trump, who frequently claims to be victimized by powerful forces while demonizing his enemies, only helped fuel the conspiracy theory. Its acceleration was also enabled by years of distrust stemming from tales of shadowy cabals of elites — which Mr. Trump has called “the deep state” — engaged in nefarious plots.

“The result was a perfect storm of righteous fury, blame-casting and conspiratorialism, at a moment when absolutely everyone was paying attention,” said Emerson Brooking, a resident senior fellow at the Atlantic Council’s Digital Forensic Research Lab, who studies online ecosystems.

6:11 p.m.  Gunshots ring out.

6:15 p.m.  An anonymous X account pointed fingers at Mr. Biden’s “antifa,” a reference to the loosely organized left-wing anti-fascist movement, for the attack.

6:19 p.m.  A user in a Trump fan forum called Patriots.win wrote, “I guess they really do want war.”

6:33 p.m.  A pro-police group with 107,000 followers on X criticized “those who have been using inflammatory, dehumanizing rhetoric creating an atmosphere for violence.”

6:34 p.m.  Another account on X made the outlandish claims, without proof, that the Central Intelligence Agency had been involved, and also accused Hillary Clinton and Barack Obama of having tried to kill Mr. Trump.

6:45 p.m.  Laura Loomer wrote on X about President Biden’s comment to donors earlier in the week that “it’s time to put Trump in the bull’s-eye.” She did not mention that Mr. Biden had made the remark as part of an appeal to pivot public focus away from his disastrous debate performance last month and toward his political rival.

Minutes later, Ms. Loomer, who has just under one million followers on X, said that “they tried to kill Trump,” suggesting that the attack was arranged by the Democrats to take attention away from Mr. Biden’s age.

“Do I think the rhetoric led to this? Yes, I do,” Ms. Loomer said in an interview on Monday. “A bull’s-eye is a target. It doesn’t matter if it’s a different context, it’s the imagery.”

6:47 p.m.  After Ms. Loomer’s posts on X, other Biden critics seized on Mr. Biden’s “bull’s-eye” language. Representative Mike Collins, Republican of Georgia, posted on X that “Joe Biden sent the orders.” His post has been seen more than 16 million times.

7:12 p.m.  Only an hour had passed when the oldest son of Jair Bolsonaro, the far right former president of Brazil whom Mr. Trump had endorsed, weighed in. Flávio Bolsonaro wrote on X that “the left” tried to kill Mr. Trump.

8:30 p.m.  At least six Republican members of Congress had blamed the assassination attempt on rhetoric from Democratic politicians and the media. Senator J.D. Vance of Ohio, who was named by Mr. Trump as his vice-presidential pick on Monday, wrote on X that the language used by the Biden campaign “led directly” to the shooting.

The post, which has amassed 17 million views, went up hours before the F.B.I. named Thomas Matthew Crooks as its suspect on Sunday. Representative Marjorie Taylor Greene of Georgia also addressed Democrats and the media on X, posting, “YOU are responsible” and “they tried to murder President Trump” (Law enforcement have not offered insight into the motivations of Mr. Crooks, who was a registered Republican.)

11:21 p.m.  A pro-Russian account on Telegram also mentioned Mr. Biden’s “bull’s-eye” remark, alongside a photo of Mr. Trump’s wounded ear, picking up hundreds of thousands of views. RT, the Russian state television network, later went on X to amplify claims that Mr. Biden and the Democrats were at fault.

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