Police are set to go nationwide in their bid to identify human remains found on Corstorphine Hill.
Detectives have confirmed that the badly decomposed body discovered in a shallow grave by a passer-by on Thursday belonged to a woman.
Excavation work has now been completed, but the outcome of forensic tests, which may provide clues to the identity of the victim, could take several days to complete.
Officers do not believe the body is that of anyone already known to be missing.
A senior police source said: “If the body did not belong to someone who has been reported missing locally, the police will have to look further afield.
“And if it is the case the body has been buried in a shallow grave, clearly that suggests there’s been foul play.” Officers maintain it is too early to say whether the death is suspicious, but believe the remains have been lying in the beauty spot for “months rather than years”.
The source added: “The first thing police will be doing is looking at forensics to see if they can identify how long the body has been there and an approximate age.
“The body is said to have been found in a shallow grave, but sometimes what appears to be a shallow grave can be an indentation caused by the deterioration of the body.
“If they are not looking at someone from the missing persons register, they will be looking to identify the body through some other means.
“Normally there are quite a number of unidentified bodies across the UK. At any one time, there are between 20 to 30 lying in mortuaries.”
It comes as detectives ruled out speculation that the body was that of murdered bookkeeper Suzanne Pilley, who went missing from her Edinburgh home two years ago.
Her former lover, David Gilroy, was convicted of her murder last year, but her body has never been found despite extensive searches in Argyll.
Police visited the family of Ms Pilley as a “courtesy” hours after the grim discovery was made last week.
Ms Pilley’s ex-husband Peter Durrand, 50, who lives in Inverkeithing, said: “It would have been good from her parents’ perspective if her body had been found. They are getting older now.
“But the police spent quite a lot of time looking for Suzanne up in the Argyll forest and I’m not sure they would have done that if they hadn’t thought she was there.
“The detectives did seem to come out quite quickly to reassure her parents that it wasn’t her.”
The site, on the same hill as Edinburgh Zoo and popular with dog walkers, remains sealed off by police.
Detective Chief Inspector Keith Hardie, of the major investigation team, who is leading the inquiry, said: “Good progress was made over the weekend with a lot of support from a wide variety of specialists.
“The remains have been fully excavated and the detailed examination of the site will continue over the next few days. Our focus is now on trying to identify the victim and then determine the circumstances surrounding her death.”