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5 August 2015, 16:31 | Updated: 30 March 2016, 13:50
Officers were called in after a member of the public made the find in Riverside Park in Glenrothes on Tuesday afternoon.
the remains are in dense woodlands to the north of the park and the area is still cordoned off while forensic investigations are being carried out.
Once inquiries at the scene are completed, the remains will be taken away for further analysis in a bid to discover the gender, identity and cause of death.
It may be several days before the remains are removed, police said, but the park remains open to the public.
Chief Inspector Stevie Hamilton, local area commander for central Fife, said: "As part of our investigation into the discovery of these remains, we have spoken to the families of a number of missing people and will continue to update them as our inquiry progresses.
"It is essential that the examination and recovery of these remains is thorough and professional, and it may takes us several days to remove them from the area.
"I would like to thank the local community in advance for their continued patience and support.
"The process of establishing the identity of these remains and the circumstances surrounding how the individual died is likely to take some time, and until then it would be inappropriate for us to comment further.
"We will provide further updates in relation to this investigation whenever we have new information.''