VATICAN CITY — Pope Francis sped two of his predecessors toward sainthood on Friday: John Paul II, who guided the Roman Catholic Church during the end of the cold war, and John XXIII, who assembled the liberalizing Second Vatican Council in the 1960s.

In approving the sainthood of John XXIII even without a second miracle attributable to the pontiff, Francis took the rare step of bypassing the Vatican bureaucracy. Francis also said a Vatican committee had accepted the validity of a second miracle attributed to the intercession of John Paul.

The canonization cause for John Paul began almost immediately after his death in 2005. At his funeral, crowds in St. Peter’s Square began shouting “Santo subito,” or “Sainthood now,” for the beloved pontiff....