It also argues it is time to create what amount to virtual congregations, by allowing "access to the sacraments" for people who are not "physically present in the congregation".
In Presbyterian teaching, the term "sacraments" refers only to the rites of baptism and communion.
"Wider questions about membership and belonging are being asked by congregations whose services, through the internet, are being carried well beyond their parish boundaries," the paper says.
It says the idea of being a member of a congregation is becoming "blurred" as people move around yet keep strong links through new technology.
"In a world where the fastest-growing communities are being fostered online, the committee believes now is the time to open up a wide-ranging discussion on these developments," the paper states.
Norman Smith, vice-convener of the Mission and Discipleship Council, said the discussion of "the relationship with the Church when someone is online is being driven by a growing reality on the ground".
"We have an increasing number of churches with an online component and they are asking questions about what it means to belong to the Church."Telegraph Group Ltd