Greek police identified the suspect of the accused crime, Yiannis Paraskakis in a tweet and revealed he is currently in custody, charged with the rape and murder of Dr Suzanne Eaton.
Prof Eaton went missing on 2nd July while attending a conference near Chania on the island of Crete.
Her body was found six days later in an abandoned underground storage site used during World War II.
Police Major Eleni Papathanasiou, a spokeswoman for the Crete Police, said Eaton was attacked after going out for a daily walk.
Papathanasiou added: "The suspect reported that on July 2, 2019...motivated by the intention to commit sexual assault, he hit her twice with his car to stop her.
"According to his claims, he placed the victim, unconscious, in the trunk of his car and transferred her to a ventilation drain in the wartime storage (tunnel), where after raping her, abandoned her there."
Paraskakis' father has acknowledged the "heinous and appalling way" the scientist was killed.
In a letter sent to the press, the suspect's father said: "As a human being and a priest, and entirely in agreement with the prevailing sentiment, I am devastated at the heinous and appalling way one of our fellow humans lost her life, even more so that the perpetrator of this crime is my own child.
"I want to express my sincere condolences to the family, husband and children of the hapless American woman Suzanne Eaton.
"I hope God provides them strength and comfort. As long as I live, I will pray to the Almighty to rest her soul."
He added that "on the other hand, as a father, I cannot not stand by my child during this difficult time, even if he committed such a serious crime".
"I would like to apologise to the family of the hapless woman, my fellow villagers, all Cretans, and the Greek and global public opinion."
He also asked people to respect his family's "own pain at this time".
"Just like the family of Suzanne who died tragically, so shall we from now on and from here die an emotional and moral death every day," he said.​
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