Thompson, a 50-year-old father of two, was shot as he made his was to an investor conference in Midtown Manhattan where he had been scheduled to speak later that day.
Police said the gunman first fled the scene on foot, before riding a bike towards Central Park.
The motive for the killing is still being investigated. Authorities have confirmed the words “deny”, “defend” and “depose” were written on the bullet casings found close to the victim’s body – language which could be associated with critics of the US’s private health insurance industry.
On Friday, a person familiar with the matter told CBS News, the BBC’s US partner, that investigators believed the suspect was no longer in New York City and may have boarded a bus to the city of Atlanta in the state of Georgia.