A mid-term draft report issued through the meeting had called for greater openness towards gay people and divorced Catholics who have remarried.
However, those paragraphs were not approved, and were stripped from the final text.
The report will inform further debate before the synod reconvenes in larger numbers in a year’s time.
Correspondents say the text welcoming gay people and remarried Catholics had been watered down in the final version that was voted on – but it appears that they still met with resistance from conservatives.
All other parts of the draft report were accepted by the synod.
Speaking after the vote, Pope Francis told attendees that he would have been “worried and saddened” if there had not been “animated discussions” or if “everyone had been in agreement or silent in a false and acquiescent peace”, AP news agency reported.
Pope Francis also cautioned against “hostile inflexibility, that is, wanting to close oneself within the written word, and not allowing oneself to be surprised by God”.
While the earlier draft had said that gay people had “gifts and qualities to offer to the Christian community”, the revised document only said that discrimination against gay people “is to be avoided”.
The Pope said the full draft document, including the rejected paragraphs, should be published.
“Keep in mind this is not a magisterial document….the Pope asked for it to be made available to show the degree of maturity that has taken place and that which still needs to take place in discussions over the coming year,” Holy See press officer Tom Rosica said on Vatican Radio.
Pope Francis had made a powerful appeal to traditionalists not to lock themselves within the letter of the law, but conservative cardinals and bishops carried the day at the end of the synod.
About 200 bishops attended the synod on family issues at the Vatican.
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