Calls for an independent investigation have been made after BBC Scotland revealed new information about the death of two-year-old Madison Horn.
The toddler was killed by her mother's boyfriend in Fife in 2014. An official review into her death concluded it could not have been anticipated.
But the BBC found that a social worker had failed to warn Madison's mother about her new boyfriend's violent past.
The council said the review had found key information had not been shared.
Criticism of the council by Madison's mother and grandparents featured in a BBC documentary, Fife's Child Killings - The Untold Story.
The programme examined three child deaths in Fife within a four-month period in 2014 - Madison Horn, Liam Fee and Mikaeel Kular.
In light of the BBC's investigation, Conservative MSP Michelle Ballantyne and Neale Hanvey, a former councillor and former SNP lead on social work in Fife, have called for an independent review to "understand what happened".
Madison was murdered by her mother's new boyfriend Kevin Park at her home in Kelty, in April 2014.
During his trial for her murder, the court heard Park had 38 previous convictions, including for domestic abuse and other types of violence.
Park was babysitting the toddler when he attacked her, beating her with a pool cue and slamming her head against a wall.
Doctors found 65 separate injuries on Madison and she died later in hospital.
A Significant Case Review into Madison's death, commissioned by Fife Council Child Protection Committee and published in August last year, concluded: "The review team found that the death of child A (Madison) could not have been anticipated.
"There was no evidence to suggest that any agency was aware of any concern regarding the child's wellbeing at the time or previously. Neither child A, nor her mother were known to Social Work at the time."
However, a BBC investigation found a separate document from the social work watchdog, the Scottish Social Services Council (SSSC), which revealed Park's social worker was aware he was in a new relationship with Madison's mother, Annemarie White.
The social worker was supervising Park's Community Payback Order - an electronic tag.
The document, referring to Park as "AA" and Madison's mother as "BB", said the social worker had failed to "ensure AA's new partner, BB, was fully aware of the potential risks AA posed to women and children".
It concluded: "BB and Child A were placed at an increased risk of harm as a result of your failure to ensure BB was fully aware of AA's background and your failure to notify relevant parties and other agencies about AA's new relationship."
The report does not mention that Madison Horn died at the hands of Park.
The SSSC found Park's social worker guilty of misconduct and he had a warning placed on his registration.
The BBC has also established that social workers had visited Park's old home on two or three occasions to assess whether he posed a risk to other children, but there was no similar assessment in Madison's case.
Annemarie White - who had been in a relationship with Park for five months before he killed Madison - told the BBC: "Kevin Park has ruined my life by taking Madison away from me."
She said if she had known the nature of Park's previous convictions she would not have been in a relationship with him.
"To answer your question if I think that social work failed to protect my daughter, then yes, I do," she said.
"I think they could have done more to protect, and maybe she would have still been here today if they'd done their job right in the first place.
"Maybe I would've been able to prevent it if I'd known more. So yes, the system failed."
Madison's grandparents also believe more should have been done by the social services department.
Grandmother Alexis Munro said: "If they knew he was like that, why was Madison not protected and why were people not going in to make sure Madison was all right?"
Grandfather Thomas Haldane said: "My granddaughter suffered because a social worker basically did not put a report on a file because a criminal was getting his tag moved from one house to another address.
"Madison was just left at that monster's mercy.
"So for Fife social work services to say 'nothing could be done to prevent this tragedy' - it's just not true."
Fife Council refused requests for an interview. Its chief executive, Steve Grimmond, said: "The Significant Case Review into Madison's death was led independently by Safaa Baxter. Her report concluded that Madison's death could not have been anticipated.
"As part of the Significant Review Process, the independent reviewer met with Madison's mother and fully considered Kevin Park's offending history, which included his involvement with Criminal Justice services.
"The review concludes that key information was not shared as it should have been. We deeply regret what happened to Madison and all necessary steps have been taken to minimise the risk of something like this happening again."
Former councillor Mr Hanvey told the BBC an investigation was needed.
He said: "I think an independent review, headed up by a competent professional, supported by lay members, should begin an immediate investigation into the allegations that this programme is making, and into the wider implications of that in terms of if there was a deliberate attempt to obfuscate the facts around the Madison Horn case."
He added: "We don't have an isolated situation. We've got multiple child deaths in the one authority, and I think that, given this information and that situation, make the case unanswerable.
"We need to understand much more detail, and in a much more honest and transparent way, what exactly happened here."
Tory politician Ms Ballantyne told the BBC: "I think it is quite clear an independent inquiry is needed in this case, the documentary raised some difficult issues that need to be looked at - it is time we stopped sweeping them under the carpet and we actually looked into it in proper detail."
The programme also hears concerns from the grandparents of Mikaeel Kular about how Fife Council handled their contact with them.
Three-year-old Mikaeel was killed by his mother Rosdeep Adekoya in January 2014.
Her stepfather, Dr Bangarpet Krishnaswamy, said the family contacted Fife Council social services two or three times with concerns about Rosdeep's children's welfare, but they felt excluded from any decision making process about their future.
Despite their close involvement in the children's lives they said they felt "eliminated from the scene".
The family also have concerns about the Significant Case Review into Mikaeel's death.
Dr Krishnaswamy said he had to initiate involvement with the SCR and that the family were not happy with the findings because it did not answer their key questions.
He said: "When the review body was set up, I wrote to them and said I'd like to explain some of my concerns. Until then they didn't contact me. I made the contact."
He also believes these types of investigations do not promote a culture of learning and should be more public and independent.
"We're all capable of making mistakes and in a big structure it will happen more often, but there seemed to be a lack of accepting that the council need to be upgraded in their knowledge," he said.
"I think we should develop a culture happy to disclose details."
In response, Fife Council said: "The central finding of the independent review states that the circumstances that led to Mikaeel's death could not have been predicted.
"Members of the wider family were contacted as soon as possible at start of the SCR process by the independent reviewer, although there had also been some pro-active contact before the end of the trial.
"The report is clear that good communications existed. Staff acted well with the information available to them at the time."