The only clue to the boy's identity was his shorts
Police said they received a number of calls from members of the public trying to be helpful.
But they said the calls offered no new leads as to the identity of the young boy or his killer.
The torso of the Afro-Caribbean boy, said to be aged about five-and-a-half, was spotted by a passer-by near Tower Bridge last Friday.
No-one has come forward to report the child missing, and a police search of all the missing person's records has been unsuccessful.
Divers have been searching the Thames and members of the public have been urged to look out for the boy's head, arms or legs being washed up from the river.
Dutch case
The boy had been wearing orange shorts labelled Kids and Company, which had been made for retail in Woolworths in Germany.
A post-mortem found he died from a "violent trauma to the neck", and his head and limbs were removed after death.
Police said the body had been cut up with a sharp-bladed instrument.
The body is thought to have been in the river for between one and 10 days.
Detectives investigating the death have met their Dutch counterparts who are working on a similar case, where the torso of a young girl was found in a lake.
But a police spokeswoman said there was no clear link between the deaths.