Cole Allen thought he was “Rambo” and armed himself “to the teeth” to try to kill President Trump at the White House Correspondents’ Dinner, DC’s top law-enforcement official revealed Sunday.

Jeanine Pirro, US attorney for the District of Columbia, stressed it wasn’t friendly fire but Allen, 31, who shot a Secret Service officer when he stormed the Washington Hilton last month, and that she is confident her team can prove the “brilliant Caltech grad intended to kill Trump.

“Clearly, the president is a target. And make no mistake, it is not just the manifesto. It is his actions,” Pirro told CNN’s “State of the Union,” referring to Allen’s alleged hate-fueled missive in which the mechanical-engineering grad and former NASA intern outlined his violent plans while calling himself the “Friendly Federal Assassin’ Allen.”

“I mean, this guy thought he was Rambo,” said Pirro, who was among the administration officials at the dinner at the time of the shooting.

“I mean, he was armed to the teeth.

“And he takes a picture of himself. He is smug, he is proud, and he is focused on what he’s doing,” she said, noting selfies the suspect took in his hotel before the shooting.

Allen, the son of a church leader, was armed with a shotgun, handgun, and knives when he stormed the security perimeter a floor above the ballroom where Trump, administration officials and hundreds of reporters were on April 25, according to authorities.

In the suspect’s alleged manifesto, which was first revealed by The Post, he stated his targets were “Administration officials (not including [FBI chief] Mr. [Kash] Patel): they are targets, prioritized from highest-ranking to lowest.”

The manifesto did not mention Trump by name, though there was one line that said, “And I am no longer willing to permit a pedophile, rapist, and traitor to coat my hands with his crimes.”

Pirro was unsure about whether that was a reference to Trump when asked about it Sunday.

“You’re going to have to ask him that. I don’t really care,” she said, referring to Allen.

“I think if you read the manifesto … it is very clear who the intended target is. It is very clear, based upon the fact that as soon as this president said that he was going to be at the Hilton for the White House Correspondents’ Dinner on March 2nd, [Allen] then made the decision to hatch the plan,” Pirro said.

“I can tell you, we will be able to prove that beyond a reasonable doubt,” she said. “The one issue that people might think about is, is he insane. He is far from insane. He is brilliant. He has a master’s degree. He work[ed] at a NASA Jet Propulsion Laboratory.”

Another question that swirled over the White House Correspondents’ Dinner shooting was who shot the Secret Service officer in his bulletproof vest, causing a minor injury.

Early on, some observers speculated it may have been friendly fire. Officials had claimed that a Secret Service agent fired five rounds when Allen stormed through the security checkpoint.

But Pirro was emphatic that Allen was the one who shot the agent.

When asked if the feds determined who shot the agent, Pirro responded Sunday, “We have.

“There’s video of the defendant shooting at the Secret Service agent. We now can establish that a pellet that came from the buckshot from the defendant’s Mossberg pump-action shotgun was intertwined with the vest of the Secret Service officer.

“It is definitively his bullet,” she said, referring to Allen.

Allen is facing charges of attempting to assassinate the president of the United States, discharging a firearm during a crime of violence and transporting a firearm and ammunition in interstate commerce with intent to commit a felony.

He was arraigned last week and did not enter a plea at the time.

Pirro was present at the Washington Hilton during the shooting.