If the tribe of Levi ascended Har Gerizim how could they also stand in the middle and recite the B'rachos and K'lalos?
Sotah, 37a: It was either the elders of the Kohanim and the Levi'im who stood with the Aron, or all those who were fit to serve.
Following the Lashon of the Pasuk there - and the Pasuk here refers to them as 'ha'Levi'im', since it is one of the twenty-four locations where the Torah refers to Kohanim as 'Levi'im' - See Yevamos, 86b. The Gemara in Sotah, 32a however, states that the Kohanim surrounded the Aron, and the Levi'im, the Kohanim. See Tosfos there, 37a DH 'I Efshar'.