The Mishnah (30b) lists the kriat hatorah for each yom tov, rosh chodesh, fast day, and ma’amad. For a source, the mishnah writes “as it says ‘And Moshe declared the holidays of Hashem to Bnei Yisrael’(VaYikra 23:44) to read each one of them in its time.” Since the Mishnah quotes a pasuk from the Torah, the Bach (OC 685) writes that the obligation to read the Torah on Shabbat and Yom Tov is d’oraita, from the Torah itself. However, Tosafot (17b d’’h kol) writes explicitly that the obligation is only d’rabbanan, rabbinic. According to Tosafot, this pasuk is not the actual source for the halacha, but rather it is an asmachta, a support, hint or reminder that Chazal used for their new takanah.

The Rif quotes the Talmud Yerushali that has a related discussion. It says that “Moshe established (tiken) for Israel that they should read from the Torah on Shabbos, Yom Tov, Rosh Chodesh, and Chol HaMoed, as it says ‘Moshe told the holidays…’” At first glance this seems to support the Bach, since it says that krait hatorah on Shabbat and Yom Tov goes all the way back to Moshe Rabbeinu, implying that it is d’oraita and not d’rabbanan. However, one could argue just the opposite. The Yerushalmi says that Moshe “established” kiat hatorah, a wording that almost always refers to a d’rabbbanan halacha. It is true that Moshe received the Torah from Hashem at Har Sinai, but he also had the authority to create d’rabbanan takanot like any other later beit din. Tosafot would argue that krait hatorah on Shabbat and Yom Tov is an example of a d’rabbanan halacha that Moshe Rabbeinu established.