Federal officials said Thursday that the gunman who shot three detainees at an Immigration and Customs Enforcement field office in Dallas had been aiming for immigration agents, pointing to notes that they said he had left at his home that showed a hatred of the federal government and a desire to cause immigration agents “real terror.”

Nancy Larson, the acting U.S. attorney for the Northern District of Texas, said at a news conference in Dallas that the actions of the gunman were the “very definition of terrorism.”

The briefing appeared to try to resolve what had been a lingering question of a motive behind the shooting on Wednesday, in which no law enforcement officers were hurt but one detainee was killed and two others were injured. The gunman, identified by the authorities as Joshua Jahn, 29, killed himself.

Ms. Larson said that Mr. Jahn “very likely acted alone” and had left many notes, which investigators found while searching his home. One read, “‘Yes, it was just me.,’” and another referred to ICE agents as “people showing up to collect a dirty paycheck,” according to Ms. Larson.

Ms. Larson said that the notes indicated that he did not intend to harm or kill any detainees, saying that it was a “tragic irony” that detainees were struck. Officials on Thursday said the detainees who were shot had been restrained in a transport van and could not escape the gunfire, though Marcos Charles, who leads enforcement and removal operations for ICE, hailed the efforts of agents at ICE and the Bureau of Alcohol, Tobacco, Firearms and Explosives for their actions to save other detainees.

The officials declined to identify the detainees who were struck in the shooting. One of the wounded who was hospitalized is a Mexican citizen, according to the government of Mexico.

The gunman legally obtained the gun used in the shooting — an 8-millimeter bolt-action rifle — last month, according to Joseph Rothrock, the special agent in charge of the Dallas field office of the F.B.I. He said there was a “significant, high-degree of pre-attack planning.”

The details released by federal officials indicated that the shooting on Wednesday had been part of a pattern of violence against federal immigration officials, including two July shootings in Texas, at a detention center in Alvarado and at a border patrol facility in McAllen.

Earlier on Thursday, the director of the F.B.I., Kash Patel, on social media linked the shooting in Dallas to the assassination of Charlie Kirk, saying the Texas gunman had searched for video of Mr. Kirk’s killing in the hours before opening fire early Wednesday morning.

Mr. Patel also referred to one of the gunman’s notes that suggested his gunfire early Wednesday morning had been meant for the agents at the office and not the detainees who were ultimately struck.

Mr. Patel wrote in his post that the note said, “Hopefully this will give ICE agents real terror, to think, ‘is there a sniper with AP rounds on that roof?”

An image of rounds found near the Dallas gunman was released by Mr. Patel on Wednesday, including the words “anti-ICE” written in blue on one of the rounds.

Mr. Jahn displayed little public sign of having adopted a violent or even a strong political position on immigration or other issues. What he did appear to have in common with other recent gunmen were struggles adjusting to adulthood and growing social isolation.

After graduating from high school near his family’s home in Fairview, Texas, a northern suburb of Dallas, Mr. Jahn took courses at a local community college but appeared to never graduate. He struggled to hold retail jobs for more than a few months at a time.

Public records show that Mr. Jahn had a charge for selling marijuana in 2015. A couple years later, he drove more than 1,000 miles northwest to Washington, after seeing an internet advertisement for a seasonal job on a marijuana farm. He spent months essentially homeless there, said Ryan Sanderson, the owner of the marijuana farm, in a telephone interview.

“He was just a weirdo,” Mr. Sanderson said. “He drove all the way from Texas for a temporary job, and was living out of his car.”

Mr. Sanderson said he had employed Mr. Jahn for a few months as part of a group of about 15 workers, which was longer than he usually did for the seasonal work of picking marijuana leaves from plants in an indoor facility.

“I actually kept him longer than everybody else, because I did feel bad for him,” he said. “I could tell he was just lost.” Ultimately, Mr. Sanderson said he could no longer keep him on, in part because Mr. Jahn was not a reliable worker.

He said he had never heard Mr. Jahn discuss anything political.

“Back then, there was no politics,” he said. “We all had a good time, we worked together.”

After returning to Texas, Mr. Jahn found work for a company that installs solar panels on rooftops in 2019. His employment there ended after “less than a few months,” according to a company representative.

Margarita Birnbaum contributed reporting from Dallas and Durant, Okla.