The decision to censure the Episcopal Church of the US for consecrating gay bishops and allowing clergy to perform same-sex marriages was "fair", according to its Presiding Bishop Michael Curry.

Bishop Curry said the vote by Anglican Archbishops from around the world to remove the Episcopal Church from votes on doctrine and from representing the Anglican Communion on ecumenical and interfaith bodies was a "very specific, almost surgical approach".

He told the National Press Club that he welcomed it because it allowed the differing provinces of the Communion to voice their differences while remaining part of one body.

He said: "There was clarity on our part, both about who we are as a church and about our love and commitment to the communion and there was clarity on their part that they disagreed with us. But they didn't vote us off the island," Religion News Service reported.

After the Primates' Meeting in Canterbury, Archbishop of Canterbury Justin Welby apologised for the hurt and pain caused to the gay community by the Church.  He also denied that "sanctions" had been issued against the Episcopal Church and said that instead, it was faced with the "consequences" of its actions.

Among those at the meeting was Archbishop Foley Beach of the Anglican Church in North America, not formally part of the Anglican Communion but who represents conservative Anglican churches who have refused to follow the Episcopal Church down a more liberal path. After the meeting he said: "I participated fully in the meeting, where the first and primary agenda item was addressing the Episcopal Church's changes to the doctrine of marriage. We spent most of the week discussing this issue and seeking to come to a common conclusion.

"We unanimously agreed that these changes 'represent a fundamental departure from the faith and teaching held by the majority of our Provinces on the doctrine of marriage,' and we wrestled with what the consequences should be."

He also said that although the "sanctions" were strong, they were not strong enough. "To my deep disappointment, they didn't include the Anglican Church of Canada as they should." The Anglican Church of Canada is due to vote in July on whether to change its canon to allow same-sex marriage.

Bishop Curry's address last night at the National Press Club was entitled: "Is there room enough for all? The Church's role in creating an Inclusive World."

He said: "One of the most important statements of our time was given by Dr Martin Luther King Jr. when he said we must learn to live together as brothers and sisters or we will perish together as fools – the choice is ours: chaos or community.

"He was right when he said that in the late 1960s and the sentiment is even more profoundly true now. We must learn to live together even in the midst of intense disagreement and profound diversity. We will either create beloved community or a horrific catastrophe. Religious faith must be a positive force toward that end – and that is what Jesus of Nazareth came to show us."

He said he could understand why most of the primates voted to censure his Church.

"Because we differ on the core doctrine, it would not be seen as appropriate for us to represent the Anglican Communion in ecumenical, interfaith leadership. That's fair."

He said the Episcopal Church believed in same-sex marriage "because the outstretched arms of Jesus on the cross really are about embracing and welcoming us all." In spite of the censure, the Church will not go back on its actions, he added. "We're not changing."

Later, in his Lent message, Bishop Curry said that to be a follower of Jesus was not without struggle. "It is not easy. The truth is, this movement is difficult. It's hard work. It's work of following Jesus to the cross. And it's work of following Jesus through the cross to the Resurrection. To new life. And new possibility. That is our calling. That is the work of the movement. To help this world move from what is often the nightmare of the world itself into the dream that God intends."