Ms Hughes' letter to the authority says: "It is crucial that the root causes of these failings are fully explored and that the capacity and capability of the council and its key partners to drive improvement in these areas is fully assessed."
Of the seven deaths being examined in serious case reviews, two of the children were murdered by their fathers and four were less than one year old at the time of their deaths.
The findings of a review into the death of 16-month-year-old Amy Howson are expected to be published next year.
The baby's father, James Howson, 25, was told he must spend a minimum of 22 years in prison after he was found guilty of murdering his daughter in the town.
Amy's spine was snapped in two by Howson, a jury heard.
The baby's mother, Tina Hunt, 25, was given a 12-month suspended sentence after admitting cruelty.
The findings of three reviews have already been published - they involved children who were abused or neglected before they died.
In each case it was found social workers had missed opportunities to intervene and one review described the children's services department as chaotic and dangerous.
Children's and families minister Lady Morgan said: "It's very important that whenever there is a serious incident, or the tragic death of any child, that a proper evaluation is made of what lessons could be learned.
"And that's what these serious case reviews are all about. And that's why when Ofsted found that these reports weren't being conducted to the highest standards, that's why we took action."
Councillors have now called a special meeting to discuss the situation on Tuesday.
The mayor said: "I'm disappointed to a certain extent that politicians are raising these issues in this way.
"Children's services and the protecting and safeguarding of children is one of the most important things we do in Doncaster and they shouldn't become the centre of a political football."
However, Mr Winter said he was aware inadequacies existed and said an internal independent investigation would begin on Wednesday.
"As mayor of Doncaster, nothing is more important than ensuring the protection of vulnerable children and young people across the borough.
"I am certain we are the only council to have assessed ourselves as inadequate, which is why we are conducting our own internal and independent investigation commencing on Wednesday to find out why we have experienced such difficulties in our delivery of child safety and, crucially, how and what lessons can be learned."
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