Bishop Robinson was consecrated in 2003 amid protests
The first openly gay Anglican bishop has accused the Archbishop of Canterbury of failing to confront critics of his appointment.
US bishop Gene Robinson, who has received death threats, said Rowan Williams's handling of rhetoric against gay Anglicans could endanger them.
He said God was "very disappointed" in the way Dr Williams had failed to confront Nigeria's Archbishop Akinola.
He also said Dr Williams had criticised the US church but not others.
BBC correspondent Robert Pigott said the archbishop has, in fact, spoken out against inflammatory language.
Earlier this month, Dr Williams denounced what he called disgraceful death threats against members of a gay Anglican group, he said.
But in an interview with BBC News Hardtalk programme, Bishop Robinson said he believed God would be disappointed with Dr Williams, the nominal head of the worldwide communion.
Gene Robinson, an openly-gay divorced father-of-two, was elected bishop of New Hampshire in 2003, but his appointment was heavily criticised.
He says that since then numerous death threats have been made against him and he now wears a bullet-proof vest for some public appearances.
One of the gay bishop's fiercest critics is Archbishop Peter Akinola, chairman of the Council of Anglican Provinces in Africa, which claims 37 million members.
Asked why he thought Dr Williams had not held Archbishop Akinola to account, Bishop Robinson said: "Well, you have to ask him that - and I think he will have to answer to God about that.
"I believe [Dr Williams'] unwillingness to confront Peter Akinola and others like him who've made statements that I think any reasonable person would find over the edge - I believe God is very disappointed in that."
He also said Dr Williams should be more consistent, saying he had criticised the Episcopal Church but not given his views on other churches.
In the interview to be broadcast later on Wednesday, Bishop Robinson added that the rhetoric used by the US religious right against gay and lesbian people was treating them "as if we are sub-human".