Children of the Abrahamic covenant—those who are the literal seed of Abraham and those who are adopted into his family—have the right to receive the gospel, blessings of the priesthood, and eternal life, predicated upon acceptance of the Lord and obedience to His commandments.
Doctrine and Covenants 124:58
58 And as I said unto Abraham concerning the kindreds of the earth, even so I say unto my servant Joseph: In thee and in thy seed shall the kindred of the earth be blessed.
President Russell M. Nelson said:
“Precisely as promised, the Master appeared in these latter days to renew the Abrahamic covenant. To the Prophet Joseph Smith the Lord declared: ‘Abraham received promises concerning his seed, and of the fruit of his loins—from whose loins ye are, . . . my servant Joseph. . . . This promise is yours also, because ye are of Abraham’ (D&C 132:30–31). . . . The Lord also told the Prophet Joseph Smith: ‘As I said unto Abraham concerning the kindreds of the earth, even so I say unto my servant Joseph: In thee and in thy seed shall the kindred of the earth be blessed’ (D&C 124:58). . . . We are also children of the covenant. We have received, as did they of old, the holy priesthood and the everlasting gospel. Abraham, Isaac, and Jacob are our ancestors. We are of Israel. We have the right to receive the gospel, blessings of the priesthood, and eternal life. Nations of the earth will be blessed by our efforts and by the labors of our posterity. The literal seed of Abraham and those who are gathered into his family by adoption receive these promised blessings—predicated upon acceptance of the Lord and obedience to His commandments.”
(“Children of the Covenant,” Ensign, May 1995, 33, 35.)