Damian Hinds has told headteachers that parents do not have a veto over what is taught in schools amid concerns over protests about how LGBT lessons are taught.
The education secretary has said that schools should listen to parents views on relationships and sex education (RSE) but backed school leaders and teachers to make the right decisions.
He has written to the Paul Whiteman, the general secretary of the NAHT headteachers' union, following a meeting between NAHT and Department for Education officials.
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The NAHT has raised concerns about the protests against LGBT lessons in primary schools, which started at Parkfield School in Birmingham and have spread to other parts of the country.
In the letter, Mr Hinds said he was very concerned about teachers feeling intimidated following “the issues we have seen in Birmingham".
It comes as it emerged that Parkfield's assistant headteacher Andrew Moffat, who developed the No Outsiders Programme at the heart of the controversy, has received a death threat.
Mr Hinds also defended the government’s changes to RSE.
He said: “It is important that we continue to work hard, in partnership with you, to dispel myths and reinforce the fact that these important changes to relationships education (and RSE) will ensure all children learn about the wide variety of relationships in society throughout their school careers.
“I want to reassure you and the members you represent that consultation does not provide a parental veto on curriculum content. We want schools to consult parents, listen to their views, and make reasonable decisions about how to proceed (including through consideration of their wider duties) – and we will support them in this.
"We trust school leaders and teachers to make the right professional choices and act reasonably when considering consultation feedback, and are clear that dedicated public servants faithfully discharging their duty have an absolute right to feel confident and safe.”
On Sunday Mr Whiteman said that teachers should “be supported and protected for teaching tolerance” adding: “It’s not just what the law says, it’s the right thing to do.”
He has welcomed Mr Hinds' letter today.
He said: “We are pleased to see the Secretary of State making his views known and re-affirming the expectations that the Equality Act places on schools. It is important for the Secretary of State to show leadership and provide clarity.
“This letter confirms that while school leaders are required to involve parents and the wider community in the planned content of the curriculum, consultation does not provide parents or others with a veto on curriculum content. Schools that take this approach will receive the full support of the government.
“The Secretary of State also makes clear that ‘dedicated public servants faithfully discharging their duty have an absolute right to feel confident and safe.’ This is as it should be. Petitions calling for staff to be sacked or asked to resign are clearly unacceptable."
The NAHT is writing to its members with guidance making clear they have a legal duty to teach about same-sex families in primary schools and about sex education in secondary schools.
In recent weeks, Parkfield Community School in Birmingham has been at the centre of controversy over its No Outsiders programme of lessons, which teaches pupils about diversity, acceptance and equality.
Some parents at the majority-Muslim school have held demonstrations against the lessons, and against assistant headteacher Andrew Moffat, who organised the project.
Last month, the BBC Asian Network revealed that parents in Manchester, Oldham, Blackburn and Bradford were being organised to campaign against LGBT content.