Detectives investigating the discovery of a torso in a bin liner on a beach believe other body parts may have been dumped nearby.
The body, without head, arms and legs, was found by a group of foreign students at Southsea, Portsmouth, Hampshire, at 5.30pm on Tuesday.
Police said the torso is that of a man but a post-mortem examination conducted on Wednesday evening failed to determine a cause of death.
Identifying the victim - who had suffered a "sustained and violent assault" before death - was proving "extremely difficult", Hampshire Police added.
Detective Chief Inspector Dick Pearson, of the Hampshire Constabulary major investigation team, said: "This is a murder inquiry.
"The fact that we are unable to use more conventional methods to identify the victim, such as fingerprints or dental records, is challenging.
"The inquiry is open to the possibility that the murder may have taken place away from the local area.
"Other body parts or items linked to the murder may have been discarded in the area.
"If you notice a suspicious package that may be linked to this inquiry do not open it, but contact police immediately."
Anyone with information is asked to call Hampshire Police on 101, quoting Operation Nimbus, or Crimestoppers on 0800 555 111.