A personal prelature is a Church jurisdiction without geographical boundaries designed to carry out particular pastoral initiatives. At present, the only personal prelature in the Church is Opus Dei.
The Society of St. Pius X was founded in 1970 by Frenchman Archbishop Marcel Lefebvre in response to errors he believed had crept into the Church following the Second Vatican Council.
The Society has had a strained relationship with the Church since Archbishop Lefebvre ordained four bishops against the will of Pope John Paul II in 1988.
The Vatican communique explained that the primary purpose of yesterday's meeting was "to present the Holy See's evaluation of the text submitted in April by the Society of St. Pius X in response to the Doctrinal Preamble which the Congregation of the Doctrine of the Faith had presented to the Society on 14 September 2011."
Although it has not been published publicly, the doctrinal preamble sets out key elements of Catholic teaching which the Society will have to agree with before re-uniting with the Church. That list almost certainly includes the documents of the Second Vatican Council 1962-65.
The response given to the preamble by Bishop Fellay in April contained some amendments to the Vatican's original text. In the intervening weeks Vatican officials have been formulating their decision. This process has included personal input from Pope Benedict XVI.
The June 14 communique said that yesterday's discussions also allowed the Vatican an opportunity to provide "explanations and clarifications" for its decision.
For his part, Bishop Fellay "illustrated the current situation of the Society of St. Pius X" and promised to give a response "within a reasonable lapse of time," the statement said.