The Department for Education has "clarified" a Twitter message which said it was "nonsense to say schools must teach gay rights".
The message prompted criticism and incredulity from other Twitter users.
Lib Dem President Tim Farron described it as "unacceptable" - others said it was homophobic.
The DfE later said what was meant that it was nonsense to say schools were being forced to teach gay rights against their will.
This referred to a Sunday Times headline about the newspaper's interview with Education Secretary Nicky Morgan which said "Faith schools 'must teach gay rights'".
In its original tweet, the DfE said simply: "Nonsense to say schools 'must teach gay rights'. We want schools to teach broad curric based on British values" - without mentioning the Sunday Times story.
It provoked much comment and confusion from other Twitter users, who complained it was a "weird thing to say" or asked why gay rights were not considered to be part of British values.
Mr Farron responded by tweeting: "Tolerance & enlightenment are key parts of our education system. That @educationgovuk tweet is unacceptable. Will be raising with ministers" while Shadow Education Secretary Tristram Hunt wrote: "LGBT rights are British values. DfE must back compulsory sex and relationship education, including LGBT rights."
Gay rights campaigner Peter Tatchell described it as "disgraceful homophobia".
In the interview, Mrs Morgan said it was "crucial" that Christian, Jewish and Muslim schools follow new rules requiring them to "actively promote" fundamental British values, such as tolerance of other faiths and lifestyles, democracy and the rule of law.
Later the DfE tweeted a "clarification", directed at the Sunday Times: "It is complete nonsense to say that schools are being forced to 'teach gay rights' against their will.
"Ofsted are rightly ensuring that schools do not indoctrinate pupils about gay people - or any other people - being inferior.
"The same goes for schools that do things like make girls sit separately at the back of the class.
"Both are practices which go directly against the fundamental British values of tolerance and respect. We believe schools should prepare all pupils for life in modern Britain. A broad and balanced curriculum is vital for this."