The child's body was found near the Globe Theatre
The child's body - minus its head, arms and legs - was spotted in the river in London by a member of the public crossing Tower Bridge at 1600BST on Friday.
Detective Superintendent Adrian Maybanks, from Scotland Yard's Serious Crime Group South, said the body was that of a black Afro-Caribbean boy of around five years old.
River police recovered the torso from the water near to the Globe Theatre on the South Bank but despite a search, no other body parts could be found.
The body is thought to have been in the river for between one and 10 days.
The victim's identity has yet to be determined but officers are checking the lists of missing children in the hope of a breakthrough.
Speaking at a press conference at Catford Hill police station in south east London on Sunday, Mr Maybanks said police would not rest until the killer was found.
Violent death
"The child died a very violent death. It's very tragic and traumatic," he said.
"At this stage I would like to reassure members of the London community that we will not rest until the person responsible has been apprehended."
Mr Maybanks said the torso was wearing orange shorts labelled Kids and Company with German washing instructions printed inside.
Motive
He appealed for anyone with information about the child's identity, or who knows of a black male child who is missing and has not been seen for some time, to come forward.
He also appealed for anyone who saw a person acting suspiciously near the water front of the Thames from Teddington to the estuary to contact police.
Detectives were keeping an open mind over a motive, he added.
A post mortem examination has been held at Poplar Mortuary where the cause of death was given as a violent trauma to the neck area.
Anyone with information can ring police at Catford Hill on 0208 853 1212 or call Crimestoppers anonymously on 0800 555 111.