The Archbishop of Canterbury Dr Rowan Williams has criticised the election of a lesbian assistant bishop in Los Angeles, saying it was a threat to the cohesion of the Anglican Church.

The Rev Mary Glasspool of Maryland, 55, is the first out gay bishop to be elected since 2003. She was selected this weekend.

But Williams said her appointment raises “very serious questions” and suggested that diocesan bishops should reject her.

Williams said yesterday: “The election of Mary Glasspool by the Diocese of Los Angeles as suffragan bishop elect raises very serious questions not just for the Episcopal Church and its place in the Anglican Communion, but for the Communion as a whole.

“The process of selection however is only part complete. The election has to be confirmed, or could be rejected, by diocesan bishops and diocesan standing committees.

“That decision will have very important implications.

“The bishops of the Communion have collectively acknowledged that a period of gracious restraint in respect of actions which are contrary to the mind of the Communion is necessary if our bonds of mutual affection are to hold.”

In July, Anglican clergy and laity in the US voted to reject a three-year moratorium on the consecration of gay clergy.

Glasspool made reference to her sexual orientation in a statement released this weekend: “Any group of people who have been oppressed because of any one, isolated, aspect of their person yearns for justice and equal rights.”

She added: “I am very excited about the future of the whole Episcopal Church, and I see the Diocese of Los Angeles leading the way into that future.”

Williams’ comments are likely to come in for criticism from liberal Anglicans and gay groups after he refused to comment publicly on the anti-gay law currently passing through Uganda’s parliament. It would mean death or life imprisonment for gays.

In a statement given to the Times last week, Lambeth Palace said he was in “intensive but private” discussions with the Ugandan Anglican Church over the bill.

But a spokesman from Ekklesia, the liberal church group, told PinkNews.co.uk that the silence was more to do with current battles over homosexuality.