Inspectors declared the authority "inadequate" at safeguarding children and young people in care or at risk.
In a detailed report, Ofsted highlighted failures in risk assessments, planning, recording of information and social worker visits, and inconsistency in providing services,
Senior managers were singled out for being "ineffective" and for failing to to provide consistent support for staff.
Children's minister Dawn Primarolo said it was "deeply concerning" that inspectors had highlighted "fundamental weaknesses" in Cornwall's children's services.
She said: "Keeping children safe is our top priority, and we will not hesitate to act where children's safety may be at risk. We always act swiftly where there is evidence that a local authority is failing to deliver children's services to an acceptable level."
Cornwall's director of children's services Dean Ashton resigned earlier this month.
An unannounced Ofsted investigation in July revealed serious concerns within Cornwall's children's services department, which sparked the detailed report.
It makes a series of recommendations, some of which must be implemented immediately, others over the coming months. An interim children's services director has been appointed.
Ms Primarolo said the Department for Children, Schools and Families has been working "urgently" with Cornwall, which has "recognised the seriousness of these concerns".
In a detailed report, published today, Ofsted highlighted failures in risk assessments, planning, recording of information and social worker visits, and inconsistency in providing services,
Senior managers were singled out for being "ineffective" and for failing to to provide consistent support for staff.
A joint statement, issued by Cornwall Council, NHS Cornwall and the Isles of Scilly, Devon and Cornwall Police and the Cornwall and Isles of Scilly Safeguarding Children Board, said they were working to implement Ofsted's recommendations.
Inspectors made a series of recommendations, some of which must be implemented immediately, others over the coming months.
The Council said it is checking with agencies to identify any individual cases where children's safeguarding services have fallen short.
It has also set up a free phone number for members of the public who have previously raised concerns about the welfare of a child and feel they did not receive a proper response.
Council chief executive Kevin Lavery insisted the authority had already taken "decisive action", appointing an interim director for children, schools and families, and an interim head of improvement.
Former director Dean Ashton resigned earlier this month.
Mr Lavery said: "We are very aware of the concerns which have been expressed over the changes to the structure of the Directorate and Richard Hubbard will be looking at this to ensure that the proposed structure is fit for purpose."
Children's minister Dawn Primarolo said it was "deeply concerning" that inspectors had highlighted "fundamental weaknesses" in Cornwall's children's services.
She said: "Keeping children safe is our top priority, and we will not hesitate to act where children's safety may be at risk.
"We always act swiftly where there is evidence that a local authority is failing to deliver children's services to an acceptable level."
An unannounced Ofsted investigation in July revealed serious concerns within Cornwall's children's services department, which sparked the detailed report.
The report warned: "Cornwall faces a significant challenge in changing the culture and practice within children's social care services to ensure safeguarding services are delivered securely."
It adds: "While front line workers demonstrated a child-centred approach to their work, ineffective leadership and a lack of clarity as to how services should be delivered have led to unsatisfactory outcomes for children and young people."
Of the department's management it says: "Management support for staff in ensuring that policies, procedures and guidance are followed is inconsistent and line managers do not provide sufficiently effective challenge to the quality of child protection and child in need assessments and plans."
Ofsted began a new system of inspections for children's services this year, which includes unannounced inspections.
Dave Ellis, independent Chair of the Cornwall and Isles of Scilly Children Safeguarding Board, said "We welcome the positive comments made by Ofsted on the role of the Board, and, in particular, the quality of the Serious Case Reviews which have been carried out.
"However we recognise the challenges faced by all the agencies working with children and young people in Cornwall identified in this report and will be working closely with our partners to ensure that all children are safeguarded effectively."
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