California man Cole Tomas Allen, 31, a tutor and amateur video game developer, was arrested at the scene of the event in Washington DC.
Trump said in TV interviews he had posted an "anti-Christian" manifesto.
"He was a Christian, believer, and then he became an anti-Christian, and he had a lot of change," Trump told CBS. "He was probably a pretty sick guy."
In a message sent to family members minutes before the attack, Allen described himself as "Friendly Federal Assassin" and railed against recent actions taken by the US government under Trump, though he did not name the Republican president directly, according to a copy obtained by The Associated Press.
Allen cited Christian theology as he said he was trying to protect those harmed by the administration's policies.
"Turning the other cheek when *someone else* is oppressed is not Christian behaviour; it is complicity in the oppressor's crimes," the manifesto read, according to an official.
Targets listed in the manifesto included administration officials - although not FBI Director Kash Patel - prioritised from highest-ranking to lowest, the official said.
The manifesto mocked the "insane" lack of security at the Washington Hilton, where the dinner was held, the official added.
"Like, the one thing that I immediately noticed walking into the hotel is the sense of arrogance," the manifesto's author wrote.
"I walk in with multiple weapons and not a single person there considers the possibility that I could be a threat."
Allen's brother contacted police in New London, Connecticut, after receiving the writings, according to a law enforcement official.
The New London Police Department said in a statement it was contacted about two hours after the shooting, by an individual who wanted to share information related to it.
The chaotic events raised fresh questions about the security of top US officials, many of whom were gathered in the hotel's expansive ballroom.
Trump seized on the attention brought by the incident to promote his planned White House ballroom as a safer venue for such events.
"This event would never have happened with the Militarily Top Secret Ballroom currently under construction at the White House. It cannot be built fast enough!" Trump wrote on Truth Social.
Allen travelled by train from Los Angeles to Chicago and then to Washington, checking into the Hilton on Friday, acting US Attorney General Todd Blanche said on multiple Sunday talk shows.
Officials have said Allen allegedly fired a shotgun at a secret service agent at a security checkpoint in the Washington Hilton hotel before being tackled and arrested.
Trump, first lady Melania Trump, Vice President JD Vance and cabinet officials were rushed out as the Saturday night incident unfolded.
The secret service agent who was shot escaped serious injury because the bullet struck his protective vest, Trump said.
Allen will be charged in federal court on Monday with assault of a federal officer, discharging a firearm and attempting to kill a federal officer, Blanche said.
Further federal indictments will be coming later, Blanche added.
A White House official said law enforcement officials who interviewed Allen's sister were told he had a tendency to make radical statements, had attended an anti-Trump "No Kings" protest and referred to a plan to do "something" to fix issues with today's world.
Trump suggested the protest might have spurred the suspect to action.
"Part of the reason you have people like that is you have people doing No Kings," he told CBS. "I'm not a king."
With AP
