The misdirected effort to unify Christians without seeking converts to Catholicism was already under way in the first half of the twentieth century. In 1929, Pope Pus XI wrote on this subject in his encyclical Mortalium Animos, in which he said clearly that:
The unity of Christians cannot be otherwise obtained than by securing the return of the separated to the one true Church of Christ from which they once unhappily withdrew. To the one true Church of Christ, We say, that stands forth before all, and that by the will of its Founder will remain forever the same as when He Himself established it for the salvation of all mankind.
His Holiness also gave the reason why such true unity is of major moment:
Children did, alas, abandon their father’s house, but the house did not therefore fall into ruins, supported as it was by the unceasing help of God. Let them return, then, to the common father of all. He has forgotten the unjust wrongs inflicted upon the Holy See and will receive them most lovingly. If, as they often say, they desire to be united with Us and with Ours, why do they not hasten to return to the Church, “the mother and mistress of all the followers of Christ?” (Conc. Lateran IV, c.5.)
Let them listen to Lactantius crying: “It is only the Catholic Church that retains the true worship. It is the fountain of truth, it is the household of the faith, it is the temple of God: If anyone does not enter it, or if anyone departs from it, he is a stranger to the hope of life and salvation. Let no one deceive himself by continuous wranglings. Life and salvation are in the balance, which if not looked to carefully and diligently will be lost and destroyed.” (Divin. Instit. 4, 30, 11-12.) [Emphasis mine.]
Another source for Mortalium Animos is Papal Encyclicals Online.