Thompson, a 50-year-old father of two, was shot on his way to an investor conference in midtown Manhattan where he was scheduled to speak later that day.
Police said the gunman first fled the scene on foot and then rode a bicycle toward Central Park.
The motive for the murder is still under investigation. Authorities confirmed shell casings found near the victim’s body had the words “deny,” “defend” and “dismiss” written on them — language that can be associated with criticism of the US private health insurance industry.
On Friday, a person familiar with the matter told CBS News, the BBC’s US affiliate, that investigators believe the suspect is no longer in New York and may have taken a bus to Atlanta, Georgia.