It is up to primary schools in England to choose what they teach about same-sex relationships, the education secretary has said.
Damian Hinds has written to head teachers saying they are encouraged to teach children about LGBT issues if they "consider it age appropriate".
He said heads should consult parents but reassured them parents had no right to veto what was taught.
It follows protests over the content of lessons in some schools in Birmingham.
Rallies have been held outside the city's Parkfield Community School in protest at the "No Outsiders" programme, which teaches pupils about diversity, including LGBT rights and issues of race and religion.
Some parents said they believed the lessons "undermined parental rights and authority" - despite Ofsted's view that the lessons at Parkfield were age-appropriate.
The school and four others in Birmingham have now suspended teaching the No Outsiders programme.
The controversy has spread further afield, with parents in Greater Manchester saying they will remove their children from sex and relationship lessons.
In his letter to the National Association of Head Teachers (NAHT), Mr Hinds says reports of teachers feeling intimidated are "concerning" and it was "regrettable that myths and misinformation" about education changes were allowed to be circulated.
He suggests listening to and understanding the views of parents as a way schools can "increase confidence in the curriculum" to help children leave school "prepared for life in modern, diverse Britain".
But he writes: "What is taught, and how, is ultimately a decision for the school."
And he adds: "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... and we will support them in this."
In response, the NAHT said its members were "encouraged" by the letter and called for parents' protests to stop.
Paul Whiteman, general secretary of the union, said: "This letter confirms that whilst 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."
He added: "There is clearly more to be done in Birmingham and in other areas where protests and disagreements have happened."
The head teacher of one school in Birmingham where protests have been held also welcomed the letter, but said the government should go further.
Referring to the education secretary, Anderton Park Primary head Sarah Hewitt-Clarkson said: "It's good he's come out and said in black and white that there is no veto for the parents on what's being taught - that's a key misunderstanding for some."
But she added that the government should have a "clear national policy" on how to teach pupils about same sex relationships rather than "leaving it up to the schools".
In England, relationships education will be compulsory for all primary pupils from September 2020. Sex education will also be compulsory for all secondary pupils from that date.