The perpetrator of the murder of UnitedHealthcare CEO Brian Thompson has fled New York, while US police have released his photo for the first time.

Police Commissioner Jessica Tisch told CNN that police released the photo because they want a "broader audience to see the photo outside of New York City."

New York Police Chief of Detectives Joseph Kenny said they are reviewing footage from around the hotel where the shooting took place in midtown Manhattan.

He said the suspected gunman rode a bicycle from the scene of the shooting in Central Park.

The person then left the park around 77th Street, still on the bike, Kenny said. Footage later shows him walking to 86th Street and Columbus Avenue, according to Kenny, before getting into a taxi that takes him to a Port Authority bus stop near 178th Street and Broadway.

"Those buses are interstate. That's why we believe he may have left New York," he said, adding that police are working to find out which bus the person may have boarded.

Kenny said authorities have video of the suspect entering the station, but "they don't have any video of him exiting, so they believe he may have gotten on a bus."

Investigators say the killing was planned. The killer arrived in New York before the fatal incident and there is a video of him about 30 minutes earlier, "walking and wandering around the hotel area before committing the murder."

"He knew what time the victim would pass. He knew which hotel this conference was going to be held in," Kenny said.

Former FBI agent Candice Long believes the killer boarded a Greyhound bus to New York to avoid tight airport security while carrying a gun.

"This is a smart guy. This is very well planned. Being on the bus, he wouldn't be conspicuous and he wouldn't have to go through all the problems that would arise at an airport," Long told CNN.

But what he didn't account for, Long said, was being asked to remove the mask by a clerk at his hotel — a moment that eventually gave investigators crucial surveillance footage of his face.

"It caught him by surprise and that could be his undoing," Long said, noting later: "The pressure is on because of that picture."

Andrew Witty, chief executive of UnitedHealth Group, the parent company of UnitedHealthcare, addressed employees in an internal video message Thursday, describing the circumstances of Brian Thompson's death as "deeply shocking and disturbing."

"I want to reiterate how truly sad Brian's tragic death is for his family, for his friends, for all of his co-workers and, frankly, for the American health care industry in which Brian was an innovator and someone who endlessly put patients' interests first to try and improve health care for everyone," Witty said.