Jane Brown, head of Kingsmead Primary School in Hackney, east London, issued the apology after a meeting with education officials and the chairman of the governors. She may face disciplinary action.
In a statement afterwards Ms Brown, 36, said: 'I am dismayed at the distress I have caused to parents, staff and pupils by the unwelcome media attention which has focused on the school.'
The controversy began after the headteacher rejected an offer of free tickets for the Royal Opera House production from the Paul Hamlyn Foundation, a charity. Pupils were also invited to stage their own version of the ballet in Hackney. Ms Brown was said to have told an organiser of the project that she did not want to involve her pupils in heterosexual culture and that Romeo and Juliet was 'a blatantly heterosexual love story'.
Gus John, director of education for Hackney council, admitted yesterday that Ms Brown had asked a representative of the Royal Opera House several questions about the content of Romeo and Juliet.
He said: 'She accepts that she was seeking to bring a series of ideological considerations to the content of that play and that was wholly inappropriate. Among those questions was something like, could it be considered that Romeo and Juliet is a totally heterosexual story?'
Ms Brown, who has been headteacher at the school in Clapton Park for just over two years, looked upset and refused to answer questions when she appeared with Ken Hanson, chairman of the governors, after the meeting.
An investigation will be carried out as quickly as possible by education officials and the findings passed on to the Kingsmead school governors. They will then decide whether to discipline Ms Brown, their options ranging from a verbal warning to dismissal.
Mr John said she had wanted to give children 'as balanced an approach to the curriculum as possible' but now accepted that such considerations should not be applied to Romeo and Juliet.
He added:'There were other issues to do with the number of staff at the school at the time and the fact that they would have had to provide supply cover for the teachers going out with the children.'
Colleagues at the school said that Ms Brown had been misunderstood and that she had not wanted to expose children to the inter-family feuding in the play, which she regarded as dramatised gang warfare.
But John McCafferty, leader of the Labour-run council and an English teacher, said: 'I am currently teaching this great play to my 13-year-old English pupils. It is one of Shakespeare's best-known and best-loved plays.'
Pat Corrigan, chairman of the education committee, described Ms Brown's action as 'an act of ideological idiocy and cultural philistinism betraying no knowledge either of great art or of equal opportunities'.
Sandra Curtis, whose eight-year-old son, James, is a pupil at Kingsmead, said: 'It's just not fair to the kids. She was not considering the kids. She was only considering what she feels.'
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