Mr Cameron wants the Serious Case Review published in full.
Conservative leader David Cameron has called again for the Serious Case Review (SCR) into the Edlington torture case to be published in full.
Mr Cameron said releasing only a summary report gave a sense of an "establishment stitch-up", where the public could not see what went wrong.
Prime Minister Gordon Brown has said publishing the report's full results may identify vulnerable children.
Two brothers were detained indefinitely last week for the attack on two boys.
As the row continued, the Audit Commission announced it is to carry out a snap inspection into Doncaster Council, in light of "serious concerns" about its performance.
The SCR into the Edlington case identified multiple failings by nine different agencies and says 31 chances to intervene were missed over 14 years.
The case involved "prolonged sadistic violence" and sexual humiliation by the 10 and 11-year-old brothers on their victims aged nine and 11. They must serve a minimum of five years.
Mr Cameron said he believed publishing SCRs in full would lead to a greater understanding of what went wrong and result in quicker action to prevent such events from happening in the future.
"There is a sense at the moment that it is a sort of establishment stitch-up where all the people who have taken part in this issue are not named, they are not having to take proper responsibility, the public isn't able to see what has gone wrong and the pressure isn't there to put it right."
The prime minister said lessons must be learned from the "sickening" attack in Edlington.
He added: "This terrible set of events saddens, angers and disgusts parents throughout the country."
Mr Brown said action to prevent the attacks should have been taken "far earlier".
He said Edlington was not a typical case but it was important that lessons were learned about the co-operation between social services and other authorities.
Children's Secretary Ed Balls said the idea of publishing the findings of the Edlington review was "deeply irresponsible and would put children at risk in our country".
Mr Balls has agreed to meet MP Caroline Flint, whose constituency includes Edlington, to discuss her concerns about the case.
The MP for Don Valley agreed that the full SCR should not be published but called for executive summaries to "tell the story, not just the recommendations".
Meanwhile, a row has broken out over the appointment of Doncaster Council's new interim chief executive, Tim Leader.
Mayor of Doncaster Peter Davies is said to be unhappy over the appointment, which he believes is legally flawed, and has called on Mr Leader to resign.
A meeting is being arranged to deal with the issue.
Seven children known to Doncaster Council have died in the borough since 2004, prompting serious case reviews, Ofsted inspections and a government investigation.
An Audit Commission spokesman said the decision to carry out an inspection was prompted by "serious concerns about the council's performance in the last two years and the threat to public confidence caused by recent events".
Mr Leader said: "The announcement of this inspection reflects the fact that some important services are not improving quickly enough and that strong and effective leadership is required to drive better performance.
"We have clear plans to tackle these weaknesses, and the inspection will help us identify and root out some entrenched problems and give extra impetus to transforming our business."