"But even in the Catholic Church there are heterogeneous ideas and demands in this regard," said Koch in an interview with the "Tagespost" (Thursday). "There are quite a few bishops in Germany, Switzerland and other countries who are resolutely in favour of women's ordination and are making the future viability of the Catholic Church dependent on it."
There are major differences within the Anglican Church regarding the ordination of women as priests and bishops.
The blessing of homosexual couples has also recently caused displeasure, particularly among Anglicans in Africa.
When asked what he would say to the Primate of the Anglican Church, Archbishop Justin Welby, Koch replied.
"In conversation with Archbishop Welby, I would honestly have to say first and foremost that we have similar tensions in the Catholic Church on the same issues and that we could help each other to overcome these tensions and divisions in the Anglican world community as well as in the Catholic Church."
Koch misses passion for church unity
In the interview, Koch also criticised the fact that the passion for church un ity has waned in many places.
"It often seems to me that people are largely satisfied with the ecumenical status quo and endeavour to accept each other as churches as they are today," said the Prefect of the Dicastery for Promoting Christian Unity.
"However, I am convinced that this is not the unity that Jesus asked the heavenly Father for in his High Priestly Prayer."
In view of the Russian war of aggression against Ukraine, Koch pleaded in favour of negotiations with the aim of achieving a just peace.
"It is not enough to conduct negotiations simply to find peace in the sense of silencing the weapons," said the cardinal. "As both sides have different ideas of peace, it must be clearly stated that negotiations must be about a just peace in Ukraine."
The entire war is a disaster for ecumenism.
The particular tragedy lies in the fact that Christians are waging war against Christians.
This is an "extremely bad message for the whole of Christendom".