Since 1942, when Isaac Halevi Herzog—later the first Ashkenazi chief rabbi Israel—tried to arrange a day of prayer, fasting, and mourning for the Jews of Europe, rabbis have debated whether a new day should be created on the Jewish liturgical calendar to commemorate the Shoah. (This debate is explored in Jacob J. Schacter’s online course The Jewish Meaning of Memory). Several venerable authorities objected even to the establishment of Yom HaShoah, arguing instead that the extermination of European Jewry should be included with the destruction of the two Temples and other national tragedies mourned on the fast of Tisha b’Av.
Into this debate comes the Tenth of Tevet, the minor fast day that falls today, and primarily commemorates the beginning of the Babylonian siege of Jerusalem in the 6th century BCE. Shimshon HaKohen Nadel writes:
[I]n an attempt to reach a compromise between the secular government and religious community—and in hopes of appeasing some of the opposing rabbis—the Chief Rabbinate established the Tenth of Tevet as the “general day of kaddish,” a day for the recital of the mourner’s prayer for those whose date of their death is unknown. In addition to kaddish, they decided the day should be observed like a yahrzeit, [the anniversary of a close relative’s death].
By choosing the Tenth of Tevet—one of the four fasts established by our sages to mourn the destruction of the Holy Temple—the Chief Rabbinate chose to imbue the day with a religious character and to quiet the voices who opposed the creation of a new memorial day. During the first general day of kaddish in December of 1949, the remains of thousands of Jews from the Flossenbürg Concentration Camp near Munich were buried, together with desecrated Torah scrolls, in Jerusalem, and special prayers were recited for the martyrs.
Unfortunately [the day of kaddish] was never fully adopted outside of the [Israeli] Religious Zionist community.
Read more on Jewish Press: https://www.jewishpress.com/judaism/halacha-hashkafa/asarah-btevet-as-a-memorial-day/2023/12/20/