Education Secretary Damian Hinds has said that parents who are unhappy about LGBT lessons in schools have no right of veto.
He issued the clarification in a letter to Paul Whiteman, general secretary of the National Association of Head Teachers.
LGBT issues will be taught as part of relationships and sex education lessons becoming compulsory in schools from September 2020.
Mr Hinds said there were "myths" circulating about the nature of the lessons, which he said were about ensuring all young people feel "included". Elsewhere, he said the lessons about "developing young people's understanding of the importance of healthy and respectful relationships with all people".
"It is regrettable that myths and misinformation about the forthcoming relationships education changes in primary schools, circulated often by individuals with no links to the education system, are undermining the hard work of head teachers, and the legitimate right of parents to be consulted on what their children are being taught about relationships," 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."
He continued by saying that while schools needed to listen to the views of parents and deliver the lessons in an "age appropriate" way, parents could not veto them altogether.
He said: "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."
The letter follows protests by Muslim and Christian parents at Parkfield Community School in Birmingham over LGBT lessons.
Hundreds of parents withdrew their children from the No Outsiders programme, which was later suspended at the school.