Local media reported Eaton's body, bruised and covered in burlap, was located about 200 feet from the entrance to the bunker.
The wounds were described as "defensive" in nature. The process of identifying the body took a long time and could only be completed through the use of "forensic odontology carried out by a dentist", Papadomanolakis said.
Her body was found in a network of tunnels that were used by the Nazi to store ammunition after the Battle of Crete in 1941.
In this undated photo provided by her family, showing American 59-year-old molecular biologist Suzanne Eaton. "It is not like in a shooting". Police have opened up a homicide investigation into the death.
The body of American scientist Suzanne Eaton was found inside a former Nazi bunker on the Greek island of Crete, police told CNN on Thursday.
Eaton was on the island for a science conference when it is believed that she went missing while out for a run.
Investigators, volunteers and family members spent days scouring rugged terrain in extreme heat for any sign of the 59-year-old., who was last seen playing piano at the hotel where she was attending a conference.
Nikos Papaleonidas of Greece's disaster management unit said the warren of interconnecting passageways inside the bunker had been constructed by German troops to protect them from air raids.
Police sources tell ABC News that they are still not certain where Eaton was killed. Police say she had been suffocated.
The body of Suzanne Eaton, a molecular biologist at the Max Planck Institute at Dresden University, was found on Monday near the town of Hania, almost a week after she was last seen by friends on July 2. She had a black belt in Taekwondo and had visited many countries as part of her scientific career. He added that an examination of the body Ethan was determined that she died from suffocation. Given that fact - and the tone of the institute's statement - one can not rule out that the police should be looking for several suspects.
Her remains will be returned to the United States for burial.