VATICAN CITY (Reuters) - The global Catholic Church is split on whether to allow women to serve as deacons, a Vatican document showed on Tuesday, just weeks after Pope Francis ruled out any opening on the issue.

Giving women a greater role in the male-dominated Church is one of the issues up for the debate at a summit of bishops known as the synod.

A first, inconclusive session was held last year. On Tuesday, the Vatican released a working document due to inform discussions at a second and final session in October.

"While some local Churches call for women to be admitted to the diaconal ministry, others reiterate their opposition," it said.

Noting that women deacons will not be on the synod's agenda, it said "theological reflection (on the issue) should continue, on an appropriate timescale and in the appropriate ways".

Deacons, like priests, are ordained ministers, and as in the priesthood, must be men in today's Church. Women deacons existed in early Christianity, but it is unclear what role they had.

Current-day deacons may not celebrate Mass, but they may preach, teach in the name of the Church, baptise and conduct wedding, wake and funeral services and even run a parish.

However, the Vatican document stressed the need to "give fuller recognition" to women in the Church, saying that "by virtue of Baptism, they enjoy full equality".

Known as "Instrumentum laboris", the document was presented after consultations with national bishops' conferences and Catholic institutions and associations from around the world.

Turning to another hot-button issue, the text did not include any specific references to LGBT people, but called for more inclusivity.

"A need emerges in all continents concerning people who, for different reasons, are or feel excluded or on the margins of the ecclesial community or who struggle to find full recognition of their dignity and gifts within it," it said.

In an interview with U.S. broadcaster CBS' "60 Minutes" programme recorded in April and aired in May, Francis responded with a flat "no" when asked if he was open to women deacons.

But he added that women were often playing deacon-like roles, without formally having that title. "Women are of great service as women, not as ministers," he said.

(Editing by Crispian Balmer and Helen Popper)

By Alvise Armellini