A spectator was also killed at the rally in Pennsylvania, the Secret Service said. Former President Donald J. Trump said in a post online that he had been “shot with a bullet that pierced the upper part” of his ear.

The federal authorities identified the gunman they said tried to assassinate former President Donald J. Trump at a rally in Pennsylvania on Saturday, a shooting that killed at least one spectator. Investigators declined to discuss a motive for the shooting.

At least two other spectators were critically injured on Saturday in Butler, Pa., the Secret Service said in a statement. The agency said the gunman was dead after officers responded.

Mr. Trump was escorted off the stage bleeding from around his ear, and taken to a hospital. He later said on social media that a bullet had pierced the upper part of his right ear.

President Biden gave a brief televised statement after the incident, condemning the violence as “sick.” The White House later said the president had spoken to Mr. Trump.

Here’s what to know:

Two videos posted on social media and verified by The New York Times appeared to show the suspected shooter lying motionless on the roof of a small building roughly 400 feet north of the stage where former President Donald J. Trump was speaking. Here’s a map of the site.

Mr. Trump had been showing supporters a chart of numbers about border crossings just minutes into his speech when shots rang out in two bursts. Read firsthand accounts from our reporter and photographer.

A spokesman for the Secret Service said that the suspected shooter fired “multiple shots toward the stage” and was on “an elevated position” outside the rally venue. The Secret Service and other law enforcement agencies have not yet publicly confirmed that Mr. Trump was shot in the ear, saying only that shots were fired and that the former president was “safe.”

Two law enforcement officials said that authorities recovered an AR-15-type semiautomatic rifle from a deceased man they believe was the gunman. People who attend Mr. Trump’s campaign rallies are subject to security screenings, and their belongings are typically searched for weapons.

After the shooting, Mr. Biden expressed gratitude that Mr. Trump had been swiftly evacuated and said “there’s no place in America for this kind of violence.” Mr. Biden’s campaign said in a statement that it would pause “all outbound communications” and was working to “pull down our television ads as quickly as possible.” Read more about the president’s response.

Republicans and Democrats were quick to condemn what they viewed as an apparent act of political violence. Read more about the reaction.

The Republican National Convention, where Mr. Trump will be formally nominated as his party’s presidential candidate, will proceed as planned in Milwaukee starting on Monday, according to a statement from the Trump campaign and R.N.C. officials.

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