Brian Thompson, 50, the CEO of UnitedHealth's insurance unit and a father of two, was shot from behind on Wednesday in what police described as a targeted attack.
It came just before the company's annual investor conference at the Hilton on Sixth Avenue.
Police have released multiple photos of the suspect that were captured by security cameras from around town.
They have yet to publicly identify the man, who was last seen riding an electric bicycle into Central Park.
Several media outlets have reported that police believed that he arrived in New York 10 days before the shooting on a Greyhound bus from Atlanta and checked into a youth hostel in New York City using a fake ID from New Jersey.
Reuters has not independently verified this account.
Police offered a $US10,000 ($A15,650) reward for information leading to an arrest and conviction.
UnitedHealth is the largest US health insurer, providing benefits to tens of millions of people, who pay more for healthcare than people in any other country.
Thompson joined UnitedHealth in 2004 and became the CEO of UnitedHealthcare, a unit of UnitedHealth Group, in April 2021.
Following the attack, UnitedHealth and several other health insurers including CVS Health and Centene took down pictures of executives from their corporate websites in an apparent tightening of security measures.
Centene said late on Thursday it would no longer hold an in-person investor day next week, and that the event would be streamed.
Thompson was shot just hours before UnitedHealth's investor day began on Wednesday.
"Health insurance is a big industry and a small community; many members of the CenTeam crossed paths with Brian during their careers," Centene CEO Sarah London said in a statement.
"He was a person with a deep sense of empathy and clear passion for improving access to care."
The words "deny," "defend" and "depose" were carved into shell casings found at the scene, police sources told several US media outlets.
A New York City Police Department spokesperson would not comment on the report.
The words evoke the title of Jay Feinman's 2010 book critical of the insurance industry "Delay Deny Defend: Why Insurance Companies Don't Pay Claims and What You Can Do About It."
Feinman, a professor emeritus at Rutgers University Law School, declined to comment.
Detectives believe the perpetrator was experienced with firearms based on how he slowly and deliberately carried out the shooting, CNN reported, citing police sources who spoke on the condition of anonymity because the investigation was ongoing.
Security video showed the shooter, wearing a hooded sweatshirt, ski mask and a grey backpack, walking up behind Thompson, raising his handgun and firing at his back.
Police said the gunman arrived outside the hotel several minutes before Thompson and waited for him to walk past before firing, ignoring other passers-by.
CNN, whose reporter John Miller is a former NYPD deputy commissioner, said police found a phone in an alley that the gunman ran through and also recovered a water bottle the shooter bought just minutes before the attack.
A fingerprint on the water bottle was too smudged to provide further clues about the shooter, the New York Times reported, citing a senior law enforcement official.
New York has one of the most advanced surveillance systems of any major US city, said Felipe Rodriguez, a former NYPD detective sergeant who is now an adjunct professor at John Jay College of Criminal Justice in New York.
There are thousands of cameras in New York and all feeds can be monitored in real time as well as reviewed for previous video, aided by facial recognition software.
