The Archbishop of Canterbury has taken the step amid claims the changes to the Church of England would make eventual reunification with the Roman Catholic Church almost impossible.
Around 50 years ago the two denominations started discussions about eventually becoming one again although the latest move by the CofE would be a "further difficulty" according to Justin Welby.
The letter, which was seen by The Telegraph, was also sent to the leaders of other churches.
It said: "We are aware that our other ecumenical partners may find this a further difficulty on the journey towards full communion.
"There is, however, much that unites us, and I pray that the bonds of friendship will continue to be strengthened and that our understanding of each other's traditions will grow.
"It is clear to me that whilst our theological dialogue will face new challenges, there is nonetheless so much troubling our world today that our common witness to the Gospel is of more importance than ever.
"There is conflict in many regions of our world, acute poverty, unemployment and an influx of oppressed people driven away from their own countries and seeking refuge elsewhere.
"We need each other, as we, as churches empowered by the Holy Spirit, rise to the challenge and proclaim the good news of our Lord and Saviour Jesus Christ and strive for closer fellowship and greater unity."
CofE critics of the General Synod decision say it marks the end of 2000 years of unity with the Roman Catholic Church on the issue of the top jobs.
Former Anglican bishop of Europe, Rt Revd Geoffrey Rowell, was an opponent of women bishops and told Premier's News Hour it will cause problems but discussions should continue: "It will be a new obstacle in the quest for unity.
"It will not mean the end of dialogue, but I think we have to be realist about that," he said.
He added that all Christian churches would try to overcome any problem in the attempt to become one.
He said: "The fundamental thing for all Christians is discipleship of Jesus Christ, who calls us to share in his life, to work together, and you cannot do this and walk apart."
Listen to more from the Rt Revd Geoffrey Rowell here: