Education Secretary Ruth Kelly was said by the Independent On Sunday to be engaged in an internal battle to allow Catholic adoption agencies to turn away same-sex couples.
The Equality Act bans discrimination in the provision of goods, facilities and services on the basis of sexual orientation in a similar way to rules on sex and race discrimination.
Lord Falconer told the BBC detailed regulations being discussed now should give "full effect" to that legislation, passed last year.
"We have introduced laws which prevent discrimination against people on the basis of their sexual orientation; those laws should be given full effect," he told the Sunday AM programme.
"We do take the view in this country that you shouldn't be discriminated against on that basis and think that applies to everybody, whatever your religion."The newspaper said that Ms Kelly had the backing of Prime Minister Tony Blair but was facing stiff opposition from other senior colleagues.
A spokesman for the Department of Communities and Local Government said: "We are absolutely committed to bringing forward proposals that provide effective protection from discrimination on the basis of sexual orientation."
The Department "fully recognised" the value of same sex parents, he said. "No decisions have yet been taken about the content of the regulations.
"We will bring forward regulations shortly and people will be able to judge them on the facts, not speculation or guesswork."