Alma ordained "priests" and "elders" to "preside and watch over the church." (Alma 6:1.) However, it is not clear whether this quotation means he was ordaining them to specific offices in the priesthood; the words priests and elders are sometimes used in a general way to denote religious leaders. Concerning whether or not these terms referred to specific offices in the priesthood, Elder Bruce R. McConkie has written:
In general terms a priest is a minister. One so designated (if he is a true priest) must in fact hold the priesthood; yet the designation priest, when so used, has no reference to any particular office in the priesthood. Thus among the Nephites it was the practice to consecrate priests and teachers, give them administrative responsibility, and send them out to preach, teach, and baptize. (Mosiah 23:17; 25:19; 26:7; Alma 4:7; 15:13; 23:4.) These priests and teachers held the Melchizedek Priesthood. (Doctrines of Salvation, vol. 3, p. 87.) . . .Book of Mormon prophets gave the title priest to officers known in this dispensation as high priests. That is, they were priests of the Melchizedek Priesthood, or as Alma expressed it, "the Lord God ordained priests, after his holy order, which was after the order of his Son." (Alma 13:1-20.) Since there was no Aaronic Priesthood among the Nephites in Alma's day (there being none of the lineage empowered in pre-meridian times to hold that priesthood), there was no need to distinguish between priests of the lesser and greater priesthoods. (Mormon Doctrine, 2nd ed., pp. 598-99.)
The reference referred to by Elder McConkie in Doctrines of Salvation includes the following statement:
The Nephites did not officiate under the authority of the Aaronic Priesthood. They were not descendants of Aaron, and there were no Levites among them. There is no evidence in the Book of Mormon that they held the Aaronic Priesthood until after the ministry of the resurrected Lord among them, but the Book of Mormon tells us definitely, in many places, that the priesthood which they held and under which they officiated was the Priesthood after the holy order, the order of the Son of God. This higher priesthood can officiate in every ordinance of the gospel, and Jacob and Joseph, for instance, were consecrated priests and teachers after this order. (Joseph Fielding Smith, Doctrines of Salvation, 3:87.)