We can also add as part of this exclusive information that it was not a merely fortuitous event - that is to say, many off-the-record meetings with His Holiness have taken place since his election precisely because his being at Saint Martha's House make him much more accessible and available than many previous pontiffs. No, that was not the case at all - the pope was previously duly informed and duly met Bishop Fellay. The meeting was apparently short and cordial.
The Pope has a true interest in resolving this situation, it seems to be understood by our sources.
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Note to new readers: the Society of Saint Pius X is a society of common life for priests and the formation of priests founded by Abp. Marcel Lefebvre in 1970, and it was involved in the controversial episcopal ordinations of 1988, in Écône, Switzerland. The penalties incurred by the living parties with that act were rescinded by order of Pope Benedict XVI in 2009. Doctrinal talks were conducted with the Vatican between 2009 and 2011, and the discussions fell through at the last moment on June 13, 2012. The Holy See considers the canonical situation of the Society as irregular and that, "as long as the Society does not have a canonical status in the Church, its ministers do not exercise legitimate ministries in the Church."
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Update: Italian version by Il Sismografo.
Vatican Insider has another account, with further details -- and an acknowledgment of Rorate's initial report.
Update: Italian version by Il Sismografo.
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UPDATE (05/11/14): I.Media reports that Bishop Fellay came to the Vatican with Frs. Niklaus Pfluger and Alain-Marc Nély (respectively the First and Second Assistants to the Superior General of the SSPX). On this occasion, the two assistants of the Superior General of the SSPX were present at the daily Mass celebrated by Pope Francis at St. Martha House. Afterwards Bishop Fellay dined with Abp. Guido Pozzo and Abp. Augustine Di Noia (respectively the Secretary of the Pontifical Commission Ecclesia Dei and the Adjunct Secretary of the CDF) at the refectory of the same House. At the end of the meal, Bishop Fellay briefly met the Holy Father.
Vatican Insider has another account, with further details -- and an acknowledgment of Rorate's initial report.
UPDATE (05/12/14): the SSPX has released an official response, here, denying I.Media's additions.
UPDATE (05/13/14): the Holy See spokesman also denied I.Media's additions.