The dialogue was opened after Pope Benedict XVI lifted the excommunications of four illicitly ordained SSPX bishops in 2009.
Asked in an interview with the German magazine Focus for his reaction to the SSPX's declaration of 30 June, in which they sharply criticised the Second Vatican Council and the Ordinary Form of the Mass and swore to be true to their founder Archbishop Marcel Lefebvre, Archbishop Muller said: "Enough is enough."
Bishop Rudolf Voderholzer of Regensburg said Benedict XVI had "stretched out his hand but it was not taken".