Schism over homosexuality in the Anglican Communion would not be a disaster but it would certainly be a failure, the Archbishop of Canterbury said today.

Speaking as he and 38 other Primates from Anglican provinces take part in a worldwide meeting in Canterbury, the Most Rev Justin Welby said: "Certainly I want reconciliation. Reconciliation doesn't always mean agreement. In fact it very seldom does. It means finding ways of disagreeing well and that's what we've got to do this week."

The Dean of Newcastle, the Very Rev Christopher Dalliston, is among senior churchman to sign a letter calling on the Church to repent for discrimination against lesbian and gay Christians. More than 3,200 people have now signed the letter, on top of the 105 senior Anglicans who were the original signatories.

Archbishop Welby told BBC Radio 4's Today programme: "There's nothing I can do if people decide that they want to leave the room. It won't split the Communion."

He indicated that imminent schism was not likely, however. There is a lengthy and complex process which has to be gone through if a province wishes to leave the Communion, he said. "We want to stay together to listen to each other in service to Jesus Christ and to focus on, not only the issue of sexuality, but also the huge issues that are affecting people around the world – conflict, persecution, religious violence. Those are also really important on the agenda."

However, he did note that the reality of a possible walk-out must be faced. "The Church is a family and you remain in a family even if you go your separate ways. That's always been the case and it always will be. God puts us together and we have to work out how we live with that and how we serve God faithfully in a way that shows that you can disagree profoundly and still love and care for each other."

He said the African churches were doing some "extraordinary work" around poverty and development and Aids in a way that was "quite remarkable". 

He admitted: "A schism would not be a disaster... God is bigger than our failures. But it would be a failure. It would not be good if the Church is unable to set an example to the world of showing how we can love one another and disagree profoundly because we are brought together by Jesus Christ not by our own choice. This isn't a form of club or a political party. It is something done by God."