A self-proclaimed “survivalist’’ was busted inside Trump Tower with a bag full of weapons and fireworks — and told officials he had breached security there at least once since the election, police sources said Tuesday.

Authorities “believe his story,’’ a law-enforcement source said.

Alexander Wang, a 19-year-old Baruch College student, was arrested Monday around 6:35 p.m. after strolling into the heavily guarded high-rise at 721 Fifth Ave. — the Manhattan home base of President-elect Donald Trump, sources said.

Wang was stopped by Secret Service at a checkpoint inside the building and asked what he had in the backpack, sources said.

Wang told them about his cache, and when agents checked his bag, they found out he was telling the truth, sources said.

They recovered a large hunting knife, an M100 firecracker, handcuffs, a switchblade, flashlight, 8-foot-long black rope and a garrote, sources said.

Wang — who told cops he is a Trump supporter — said he “always” carries the weapons because he’s a “survivalist” who is also into martial arts and fireworks, sources said.

The teen, who is from upstate Poughquag, told police that he “likes to use the lounge [at Trump Tower] to study” and has been to the tower with his bag of weapons more than 10 times, including two days after Trump was elected, sources said.

“His story seemed to check out,” another police source said of Wang.

A third NYPD source added that the alleged security breach “is on the Secret Service.

“The Secret Service police are handling those checkpoints.”

Wang was arrested and charged with two counts of criminal possession in the fourth degree and unlawful possession of fireworks, police said.

He was released last night on his own recognizance after his arraignment.

Wang’s public defender, Naila Siddiqui, said he carries the knives for protection, occasionally uses the garrote as a makeshift saw and forgot that the firecracker was even in his bag.

“This is some kind of misunderstanding,” said his dad, who drove down from the family home in Duchess County and refused to give his name. “I think the secret service overreacted”

He has no prior record.

Additional fireworks were found inside his dorm room at Baruch College, sources said.

A spokeswoman for Baruch said in a statement, “We will continue to cooperate with appropriate law enforcement agencies as needed.”

Additional reporting by Natalie Musumeci

Mayor Bill de Blasio is requesting up to $35 million in federal funding for security costs at Trump Tower: