Officers are searching for Swedish journalist Kim Wall, who has not been seen since she was spotted on a 60ft homemade submarine on 10 August.
A torso missing its head and limbs was discovered in Koge Bay on Monday and DNA is being compared to genetic material from relatives of Ms Wall, 30.
Police investigator Jens Moeller Jensen said the arms and legs had “deliberately been cut off”.
He said: “We do not know yet whether it is her or not.
“The length of the torso means we cannot rule out that it could be Kim Wall, but we don’t know yet.”
The results of the DNA testing are expected on Wednesday.
Danish inventor Peter Madsen has been accused of the negligent manslaughter of the 30-year-old journalist – but denies any wrongdoing.
He initially told authorities he dropped Ms Wall off on an island later on the evening of 10 August.
But he then changed his story days later when he appeared in court, saying she died in an accident on board and he dumped her body at sea in an undefined location in Koge Bay.
Search crews found the missing sub Nautilus on 11 August and Madsen was recovered from the vessel, alone, just before it sank.
Police have said they believe Madsen “deliberately” sank the submarine. It was raised to the surface and searched, but found to be empty.
Ms Wall was a freelance journalist who had met with Madsen to interview him for a feature story she was writing.
The pair were seen onboard the Nautilus by several people in waters off Copenhagen on the evening of 10 August.
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