London, England (CNN) -- The Church of England inched towards allowing women to be bishops this weekend with a vote that traditionalists warned could split the church.
The church's governing body narrowly rejected a measure that would allow parishes that oppose women bishops to have an additional male bishop.
The proposal, floated by the titular head of the Church of England, was an attempt to satisfy conservatives.
Campaigners for women bishops hailed the vote as a victory.
But traditionalists said the ballot "has made it very difficult for those who in conscience cannot accept the ministry for women priests and bishops."
The vote took place Saturday at the General Synod, the three-times-a-year meeting that sets policies for the Church of England.
Rowan Williams, the Archbishop of Canterbury and nominal head of the church, proposed the measure along with John Sentamu, the Archbishop of York.
The rejection of the compromise was greeted with a "slightly stunned silence," said the Rev. Miranda Threlfall-Holmes.
"Everyone was aware instantly of how close it was, a slight gasp from everybody, thinking, 'Oh no, we only lost that by the skin of our teeth' or 'only passed that by the skin of our teeth,'" she said Sunday.
The Catholic Group in Synod, a conservative group, said: "We deeply regret that the General Synod has decided to ignore the leadership of the chief pastors of the Church of England."
The group suggested it would continue to fight against women bishops.
"The process in General Synod is not over and we would wish to be involved in the ongoing discussions as to a way forward that includes all loyal members of the Church of England," it said in a statement.
But the campaign group Women in the Church hailed the vote.
"We're tying hard not to use the word victory, but yes it is," said Sally Barnes, a Women in the Church representative.
"You can't have a church where we're all supposed to be one in Christ and then treat women as if it's the faulty half of creation," she told CNN Sunday.
"People don't need protecting against women, it's not a Christian concept. It's not how Christ treated women," she argued.
Under Church of England rules, for a measure like the one proposed by Williams and Sentamu to pass, it needed majority support from three different groups: bishops, priests and lay leaders.
Bishops and lay leaders backed the measure, but priests narrowly rejected it, meaning it failed.
The Church of England is probably still a couple of years away from having women bishops. If this week's General Synod approves them, as it's expected to, parishes across the church then have at least a year to consider the matter before a future General Synod casts a final vote on the issue.
The Anglican Communion -- of which the Church of England is the British branch -- is the third-largest Christian denomination, with about 77 million members worldwide.
It's facing serious strains over the ordination of women bishops and gay priests, and the Catholic Church has reached out to disaffected Anglicans, raising the possibility that conservatives could leave en masse.