It's speaking after the government was accused by a Guardian columnist and teacher of trying to take land from the Church by using the Education and Adoption Bill.
The bill, currently going through Parliament, would legally require the government to take failing schools out of its current ownership and make them into academies.
Academies are charitable trusts outside of local government control which can receive money from outside individuals or businesses.
Just under one in three state schools in the UK are either Anglican or Catholic schools.
Clause 9 of the Bill recognises that the religious character of Church schools must be protected, and includes a requirement to consult with the diocese and trustees about who the sponsor for the school will be. The government is in discussions with churches about this.
Paul Barber, the director of the Catholic Education Service, told Premier: "Whilst the Catholic Education Service supports the bill's aim of increasing standards, we do not accept that conversion to sponsored academy is the only way to improve inadequate schools.
"Despite the vast majority of Catholic schools providing a high standard of education, we believe where there are inadequate Catholic schools, decisions about their future should be made at a local level in consultation with the diocese and the school's trustees.
"As one of the largest providers of education in England and Wales, dioceses have been making these decisions for more than a century, and have led the way in school improvement, often pioneering many of the methods which are in mainstream use today.
"These have included various different types of federations, school partnerships, multi-academy trusts, umbrella trusts and executive head teachers.
"By allowing for a range of approaches the various different needs and requirements of schools can be catered for, something which the 'one size fits all' approach of the current bill will struggle to provide."
The Church of England's Chief Education Officer Revd Nigel Genders said: "Church of England schools offer a focus and emphasis on the inclusive education of the whole child and the importance of character as well as academic achievement, within a Christian ethos. This is available to all.
"This large and effective stake in education is why the Education and Adoption Bill – currently the subject of media debate – still recognises the role of the Church.
"Proposed powers would mean the Secretary of State will be legally required to intervene and pass the school to an academy trust where it is rated inadequate.
"However in any circumstances Church schools must continue to operate with the same ethos and emphasis; they can't just dispense with their essential Church of England character.
"This means we will be consulted about the identity of any sponsor for any Church of England academy.
"We have not so far opposed the Bill but the details must be ironed out to allow children to continue to have access to effective education in a Church of England context."
The Department of Education told Premier: "No parent should be content with their child spending a single day in a failing school, and we have made clear that we will tackle under-performance swiftly and robustly in any institution, including Church schools.
"Where a Church school is failing we will seek to find an appropriate academy sponsor to turn its performance around. In the vast majority of cases, this will be as part of a trust run by the local diocese or other church schools.
"However if the diocese lacks the capacity to bring about the required improvement we will pair the school with a strong non-Church sponsor and ensure its religious character is protected."