That desire includes the enlargement of the European Union to the Continent's geographic limits, the Pope said.
The Holy Father expressed this idea Saturday when he received in audience the participants in the 4th Meeting of the Postsynodal Council of the Synod of Bishops' 2nd Special Assembly for Europe.
It was the first meeting held by the cardinals and prelates since the promulgation of the apostolic exhortation "Ecclesia in Europa," and the May 1 enlargement of the European Union, which now has 25 members.
The purpose of this meeting, the Pope said, is to "reflect on the reception and to take charge of a desirable better diffusion, knowledge and application of this important document, born in the synodal atmosphere of the pilgrim Church in this Europe of ours."
The meeting was also taking place at the "special moment" of the recent EU enlargement, he said. "The Church desires that such a process continue until it reaches the Continent's geographic limits, embracing all the peoples."
Because these nations, "in addition to having strong historical ties, share the same cultural and religious values," he continued.
In particular, the Holy Father expressed the desire for "a Europe of the peoples, united in respect for legitimate plurality," in which "the transcendent dignity of the human person, the value of religion, freedom, democracy, the state of law, and the distinction between politics and religion is respected."
"This Europe, based on law, oriented to respecting human and Christian values, and to solidarity in favor of all its members, especially the most needy, will become a continent of prosperity and peace, whose example will be stimulating for all peoples and nations," the Pope said.
"The Church, firm in the message of peace and hope that the Risen Lord offers it, will not cease to propose such an ideal to the European peoples at this important moment of its history" so that this project "will be the source of a better future for all its inhabitants and for the whole of humanity," he added.
The Holy Father concluded by entrusting these proposals to the intercession of the Virgin Mary, "Mother of Hope," "so that Europe, rediscovering itself, is capable of building a better future … in respect of the rights of God and of man."