NEW YORK — The gunman who assassinated UnitedHealthcare CEO Brian Thompson in Midtown wrote the words “Delay,” “Deny" and “Defend” — a supposed insurance industry mantra for delaying claims and maximizing profits — on the ammunition he fired at the insurance company head, police sources said Thursday.

Meanwhile, police on Thursday released new images of the suspect without a mask taken at an Upper West Side hostel he was staying at before the shooting in the hopes someone recognizes him. Port Authority police working with NYPD investigators believe the suspect came to Manhattan on a Greyhound bus from Atlanta on the night of Nov. 24, a source close to the case told the New York Daily News, adding that there is footage of him walking through the Eighth Avenue bus terminal.

Cops found three 9mm shell casings as well as a few live rounds that had been expelled from the pistol as he freed the jam. “Delay, “Deny” and “Defend” were written on the bullets, sources said — leading investigators to theorize the gunman may have been outraged at how UnitedHealthcare handled an insurance claim of his or someone close to him.

“That was thought out,” a police source told the Daily News about the bullets’ unique markings.

The words on the bullets referenced the title of a 2010 book, “Delay, Deny, Defend: Why Insurance Companies Don’t Pay Claims and What You Can Do About It,” by Jay M. Feinman, which focuses on how insurance companies try to avoid paying claims.

The eerie message comes as NYPD detectives continued their manhunt and zeroed in on the suspect and a motive. On Wednesday night, police executed a search warrant on an Upper West Side hostel they believe the gunman had stayed before the early-morning shooting, according to multiple sources.

“They have an idea who he is,” an NYPD source said about the gunman. “A lot of tips are coming in.”

Thompson, 50, a married father of two from Minnesota, was walking to the Residences Hilton Club on West 54th Street near Sixth Avenue to help set up an investor conference sponsored by the health insurance giant when the gunman opened fire from a few feet away. The CEO was expected to give a speech at the event, officials said.

The gunman, who was dressed in a black sweatshirt, a black face mask, black-and-white sneakers, and was sporting a large gray backpack, had been laying in wait under the marquee for the Ziegfeld Theater before crossing the street, creeping up behind Thompson and shooting him, police said.

Surveillance video of the 6:45 a.m. shooting shows Thompson, wearing a blue blazer, briskly walking down West 54th Street near Sixth Avenue on his way to the Hilton hotel when the gunman steps up behind him with what appears to be a pistol with a silencer. After firing, the gunman runs back across the street and down a pedestrian path known as 6 1/2 Avenue. The suspect’s cellphone was recovered from the pedestrian path, police sources said.

Investigators managed to backtrack the shooter’s movements and learned he had visited a Starbucks coffee shop on West 55th Street and Sixth Avenue just before the shooting. Cops recovered a water bottle the gunman drank from and were running it for prints and DNA, a police source with knowledge of the case said.

They also tracked the suspect to the HI New York City Hostel on Amsterdam Avenue and West 103rd Street, where he stayed in a fourth-floor room before the shooting.

Surveillance pics recovered at the hostel show the suspect without his mask and smiling at workers.

Cops executed a search warrant inside his room, but didn’t collect anything that could identify the suspect, police sources said.

At the same time, officers responding to tips from the public stopped a Long Island Rail Road train on the Seaford line and visited an area airport after hearing tips that the gunman had been seen, but the suspect couldn’t be found.

Images released Wednesday show the suspected gunman holding a pistol equipped with what appears to be a silencer, and another of him riding away from the scene on a bicycle.

“Based on the evidence so far, it does appear that the victim was specifically targeted, but we do not know why,” NYPD Chief of Detectives Joseph Kenny said Wednesday. “This does not appear to be a random act of violence.”

During the killing, the pistol jammed, but the gunman was able to clear the jam and kept firing before running off.

EMS rushed the CEO to Mount Sinai West, where he died of his wounds at about 7:12 a.m., police said.

The gunman sped away on a bike and disappeared into Central Park. Police recovered images of the gunman exiting the park on the Upper West Side, but he didn’t have his backpack with him.

Police were scouring the park for the backpack Thursday.

Thompson’s wife, Paulette Thompson, told NBC News that the CEO had received threats before his trip to New York.

“There had been some threats,” she told the outlet. “Basically, I don’t know, a lack of coverage? I don’t know details. I just know that he said there were some people that had been threatening him.”

Late Wednesday, Thompson’s family released a statement saying they were “shattered to hear about the senseless killing of our beloved Brian.”

“Brian was an incredibly loving, generous, talented man who truly lived life to the fullest and touched so many lives,” Paulette wrote. “Most importantly, Brian was an incredibly loving father to our two sons and will be greatly missed. We appreciate your well wishes and request complete privacy as our family moves through this difficult time.”

A $10,000 reward is being offered for information regarding the gunman’s identity.

Anyone with information regarding his whereabouts is urged to call NYPD Crime Stoppers at (800) 577-TIPS. All calls will be kept confidential.

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(Emma Seiwell contributed to this story.)

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