Ruth Kelly has rejected claims that her religious beliefs mean she will not help gay rights in her new role of minister for equality.
Ms Kelly took over most of Mr Prescott's old job
Ms Kelly said being a practising Catholic did not stop her doing her job but she would not say whether or not she thought homosexuality was a sin.
Some campaigners say her appointment suggests the government does not take gay rights seriously.
But Ms Kelly promises she will fight against all discrimination.
The Cabinet minister, whose principal job is secretary of state for communities and local government, is a member of the Catholic group Opus Dei, which features in bestselling novel the Da Vinci Code.
'No moral judgements'
Asked about her record in missing Commons votes on the age of consent, gay adoption and civil partnerships, Ms Kelly said such issues were free votes decided by personal conscience.
"I passionately believe there should not be discrimination," she told BBC Radio Five Live.
She insisted as a practising Catholic she could hold a government portfolio because she was responsible for Cabinet decisions.
Asked if she thought homosexuality was a sin, Ms Kelly replied: "I don't think it's right for politicians to start making moral judgements about people. That's the last thing I would want to do.
"What I think the question is is what are my political views and as a politician those are the ones I'm accountable for to the public.
"As a politician I think anybody should be free from discrimination and I'll fight to the absolutely end to make sure that is the case."
Gay rights campaigner Peter Tatchell told the website PinkNews.co.uk Ms Kelly's appointment suggested the government did not take lesbian and gay rights seriously.
"Tony Blair would never appoint someone to a race-equality post who had a lukewarm record of opposing racism," said Mr Tatchell.
Lorely Burt, the Liberal Democrats' women and equalities spokeswoman, said: "How can the gay community trust equal rights legislation to be properly implemented and enforced when Ruth Kelly has such an ambiguous record on gay rights?
"Ruth Kelly urgently needs to come clean about whether she agrees with her own department's policies on equality issues."