LONDON — In a sign of deepening crisis in the Church of England after it rejected the appointment of women as bishops, its spiritual leader said Wednesday that the church had ‘‘undoubtedly lost a measure of credibility’’ and had a ‘‘lot of explaining to do’’ to people who found its deliberations opaque.

The archbishop of Canterbury, the Most Rev. Rowan Williams, was speaking after an emergency meeting of bishops called to debate Tuesday’s narrow balloting by its General Synod rejecting the ordination of women as bishops, even though female priests account for a third of the Church of England’s clergy members. Female priests hold senior positions like canon and archdeacon, and some had hoped to secure appointments as bishops by 2014.