But they say it is still too early to say whether it is the remains of Swedish journalist Kim Wall.
She was last seen alive on 10 August as she departed on a trip with submarine inventor Peter Madsen.
He initially said he had dropped her off safely near Copenhagen, but has since said she died in an accident and that he had "buried" her at sea.
The body has been sent for DNA analysis, but the results will not be available until Thursday morning.
Divers continue to search the waters near where the torso was discovered, but, despite some reported sightings, other remains have not been found.
"The current situation is that there is a torso in which arms, legs and head have been removed off as a result of deliberate cutting," said Jens Moller Jensen of the Copenhagen police.
"There is nothing about the length of the torso to indicate that it is not Kim Wall, but we do not yet know."
Ms Wall, 30, was a freelance journalist who had graduated from the Columbia Graduate School of Journalism. She was based between New York and Beijing and had written for The Guardian and The New York Times.
She was reported missing by her boyfriend after she failed to return from what should have been a short trip to research a feature about Mr Madsen and his submarine, the Nautilus.
The submarine sank hours after the search for the journalist began, and Mr Madsen was charged with negligent manslaughter. Danish police believe the 40-tonne vessel was deliberately sunk by Mr Madsen, who was rescued before being arrested.
The torso was found on Monday in shallows off the densely populated Danish island of Amager, on which the Danish capital of Copenhagen is partly situated.
Mr Madsen denies any wrongdoing.
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A headless and limbless corpse found in waters off Denmark was deliberately mutilated, say Copenhagen police.