Some of the attendees have pointed to what they say is a contradiction in the rules of the synod, which takes place every few years on a different theme.
This year, two “brothers”, lay men who are not ordained, are being allowed to vote in their capacity as superiors general of their religious orders.
But sister Sally Marie Hodgdon, an American nun who also is not ordained, cannot vote even though she is the superior general of the Sisters of St. Joseph of Chambery.
“I am a superior general. I am a sister. So in theory, logically you would think I would have the right to vote,” said Hodgdon, who is also vice-president of the International Union of Superiors General (UISG), an umbrella group of Catholic nuns.
The membership of female religious orders is about three times larger than that of male orders.
A petition demanding that women have the right to vote at synods has collected 9,000 signatures since it opened online at the start of this meeting. It is sponsored by 10 Catholic lay groups seeking change in the church, including greater rights for women and gays and a bigger role for the laity.