The modern movement toward Christian unity, whose Protestant origins stem from the Edinburgh World Missionary Conference in 1910 and whose Catholic principles were formulated by the Second Vatican Council in 1964.
These principles are mainly three:
1. Christ established the Church on the Apostles and their episcopal successors, whose visible head and principle of unity became Peter and his successor the Bishop of Rome;
2. Since the first century there have been divisions in Christianity, but many persons now separated from visible unity with the successors of the Apostles under Peter are nevertheless Christians who possess more or less of the fullness of grace available in the Roman Catholic Church;
3. Catholics are to do everything possible to foster the ecumenical movement, which comprehends all "the initiatives and activities, planned and undertaken to promote Christian unity, according to the Church's various needs and as opportunities offer" (Decree on Ecumenism, I, 4).
Source: Catholic Culture.org