The move, in a decree signed by Pope Francis on Tuesday, clears the way for each of the 38 to be beatified, a step which involves being officially recognised as 'Blessed' and can lead to sainthood at a later date.
The Holy See also confirmed that Francis has approved the attribution of a miracle to a fellow member of the Jesuit order, the Irish priest and teacher John Sullivan (1861-1933), enabling him to also be beatified.
The 38 Albanians, mostly clerics or aspiring clerics, were killed between 1945 and 1974 under the isolated and dictatorial communist regime of Enver Hoxha, who declared Albania the world's first atheist state in 1967.
The bishop who was beatified, Vincens Prenushi, was the Catholic primate of Albania and rejected Hoxha's demand for the formation of a breakaway Albanian church.
He died in prison in 1949 after being tortured.
Prennushi was among seven bishops who were either executed or died in prison under Hoxha. The Church says the regime was also responsible for the deaths of a total of 111 priests, 10 seminarists and eight nuns and the destruction of 1,820 Catholic, Muslim and Orthodox places of worship.
Pope Francis paid tribute to the Albanian faithful's resistance when he visited the country in September 2014. The pontiff was visibly moved by the personal accounts of persecution he heard from a nun and a priest now in their eighties.
That prompted him to depart from his prepared speech and ask: "How were they able to resist?"
Sullivan, who was brought up a protestant in a wealthy Dublin family, is celebrated for his work with the sick and dying in the then-impoverished villages of County Kildare in the early 20th Century.
He taught at a Jesuit school in the area, Clongowes Wood College.
His supporters have been campaigning for him to be made a saint since the 1940s.
He was declared a 'Servant of God' in 1960 and made 'Venerable' by Francis, the first Jesuit pope, in 2014.
The move from being beatified to sainthood is not automatic. Sullivan will have to have another miracle attributed to him if he is to become the latest Saint John.
Beatification is possible purely on the basis of having died for the faith but promotion to sainthood requires a miracle.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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