The department also says it wants to meet Inquest to resolve the discrepancy in the figures.
Inquest director Deborah Coles said: “My fear is there could be more deaths. Neither we nor the Department of Health knows.”
In a parliamentary answer last year, Mr Burt suggested there had been only one such death recorded by the Care Quality Commission. His predecessor, Norman Lamb, said there had been none.
The Department of Health says NHS England has recorded four deaths of young people “in an in-patient setting”.
Inquest aims to support people bereaved by a death in custody or detention, including psychiatric in-patients.
Through their own casework and Freedom of Information requests, Inquest discovered at least nine young people have died in mental health units and the true number could be higher.
The only certainty is that current reporting of deaths is confused and incomplete. The NHS places nearly half of all its young psychiatric patients in private psychiatric units and these are not subject to FoI requests.
And the Care Quality Commission, cited by the the Department of Health as collecting accurate data, is only notified of the deaths of young people who have been committed to hospital or sectioned.
This omits the deaths of voluntary patients, who make up a large part of the hospital population.
Calling for statutory notification and an independent investigation when a child dies in a mental health unit, Ms Coles said: “How on earth can we learn if we don’t know the true picture and circumstances?
“If a child dies in prison, an independent investigation follows automatically. There isn’t that independent scrutiny given to these deaths.”
Inquest says in the absence of any centralised recording of child deaths it analysed the responses to 238 Freedom of Information requests to NHS Trusts, private providers, local safeguarding children boards, local councils, the Department for Education, the Department of Health and the Care Quality Commission.
Ms Coles said: “What’s been really shocking is how difficult it is to find the true picture of the number of children dying in psychiatric care.”
Panorama – I’m Broken Inside: Sara’s Story is broadcast on BBC One on Monday 11 April at 19:30 BST. Catch up on BBC iPlayer
Credit: BBC Panorama