.
Local media also reports that homicide detectives from the Greek capital of Athens have arrived in Ikaria and have taken over the case.
Police sources said the scientist's boyfriend "was very unlikely to be considered a suspect."
The ravine is about a mile from her hotel in Kerame in the north of the island, and the area has trails along steep cliffs.
'BLOOD STAINS ON BED SHEETS' Cops have told The Sun Online that blood stains found on Dr Christopher's bed sheets were sent to a laboratory for DNA testing.
According to local media, the Oxford-educated scientist's phone was still on, prompting her worried sister to urge people not to call her to save the battery.
However, Mr Chronopoulos told The Sun Online that there has been no signal on Dr Christopher's phone since 5pm on Monday.
He said: "The mobile phone company confirmed that her phone was on and that it had picked up a signal until about 5pm on Monday.
“Since then there hasn't been a signal."
Policemen, firefighters, coast guard officers, volunteers and a naval helicopter equipped with thermal imaging took part in the search operation.
Dr Natalie Christopher had been holidaying since August 3 in Ikaria’s popular Kerame area Dr Natalie Christopher has family in Cyprus Credit: Getty - Contributor An investigation is underway to find out the circumstances of her death Credit: Facebook The owner of the hotel the couple were staying at said police had sealed off the room and that Mr Ashikalis was staying with him at his house.
The unnamed hotelier told Greek media: “He is a very good lad, he’s from Cyprus. He’s lost it, he has panicked, he cannot believe it."
He described the pair as a "nice little couple" and said there was no signs of problems in the relationship.
It has emerged she made a final Facebook post just hours before she went missing, where she wrote about how "beautiful" the area was.
Writing on Sunday morning, Dr Christopher said: "Beautiful spot for swimming and deep water solo - had so much fun here today.
"Realised later there was bolted routes here too, would love to come back again to climb. Any takers?"
According to her online profile, Natalie Christopher was a researcher for the European University Cyprus in Nicosia and worked to "develop our understanding on the evolution of galaxies by fitting models to data collected from telescopes and satellites."
She was an extreme sports enthusiast and was the face of 'Cyprus Girls Can' - a campaign to encourage local women to exercise.
Her death follows the alleged rape and murder of American scientist Suzanne Eaton in Crete.
A local man has apparently confessed to the crime in which sexual assault appeared to have been the motive.
Dr Eaton was found dead in mid July at the bottom of a cave which was used by the Nazis to store weapons during World War II near Cania.
The 59-year-old mother-of-two was originally from California and lived in Germany with her husband, a British scientist.
She vanished on July 2 at some point in the afternoon and was due to attend a conference but failed to show up.
Her family believe she went out for a run, as the only things missing from her hotel room were her running shoes.
Coroner Antonis Papadomanolakis told Greece's ANT1 News that 'something complicated happened' during Eaton's death.
Dr Suzanne Eaton was found dead at the bottom of a cave in Crete last month Credit: EPA Dr Natalie Christopher's 38-year-old partner reported her missing around noon on Monday Credit: Facebook
Missing Brit Natalie Christopher, 34, found dead in ravine after vanishing while jogging on Greek island of Ikaria