Roman Catholic theologian Matthew Levering wrote the following about the New Testament evidence for the anointing of the sick; Latter-day Saints and Catholic are agreed, up to a point, about the importance of this practice:
[W]hen Jesus sends out the seventy, he commands them to “heal the sick” (Luke 10:9) and he gives them a share of his power. They return joyfully, proclaiming that they received power even over demons in Christ’s name. Their authority “over all the power of the enemy” (Luke 10:19) includes the domain of illness and mortal disease, since it is precisely in this domain that Jesus himself performs many mighty works.
In the Gospel of Mark, when Jesus returns to his hometown of Nazareth, “he laid his hands upon a few sick people and healed them” (Mark 6:5). Immediately after this, Jesus “called to him the twelve, and began to send them out two by two, and gave them authority over the unclean spirits” (Mark 6:7). The instructions that Jesus gives the twelve disciples in Mark 6 are essentially identical to those which he gives the seventy in Luke 10. The twelve disciples “cast out many demons, and anointed with oil many that were sick and healed them” (Mark 6:13).
Clearly this healing—performed with the sign of anointing with oil—constitutes a sharing in the power of Jesus, which attains its fullness in his cross and resurrection by which he conquers sin and death. The healing communications a participation in Jesus’ overcoming of sin and death, and the twelve disciples receive the power to perform this sign. The question then is whether only the twelve disciples (and the seventy) who received a direct commission from Jesus in his earthly life have the power to perform this sign.
The letter of James indicates that the answer is no. James remarks, “Is any among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord; and the prayer of faith will save the sick man, and the Lord will raise him up; and if he has committed sins, he will be forgiven (Jas 5:14-15). The ascended Lord Jesus will work through the (sacramental) sign administered by “the elders of the church” so as either to cure the illness or to “save,” raise up, and forgive the dying believe. In performing this sacramental sign, the “elders of the Church” spread the saving power of Christ’s cross and resurrection. (Matthew Levering, Was the Reformation a Mistake? Why Catholic Doctrine is not Unbiblical [Grand Rapids, Mich.: Eerdmans, 2017], 108-9)
