Does the Mormon Church maintain that it is the one true church? What does it consider the other Christian denominations?
Yes, the Mormon Church DOES maintain that it is the one true church. In the first place there are many individuals, and a number of churches, that do not believe that any one church is the exclusive Church of Jesus Christ, his kingdom on the earth, containing within its organization and membership the requisite priesthood authority to act officially in his holy name, and containing the ordinances and covenants that God has placed as requirements for man’s return to his presence.
If any church believes and teaches that it doesn’t matter to which church you belong as long as you confess Jesus Christ to be your Savior, they do not believe that God organized a church on the earth and that no Divine authority is necessary to administer in the affairs of the Kingdom. There are other churches that believe in Divine authority and, of course, believe that they have that authority. Principle among such churches are the Catholic Church and the Church of Jesus Christ of Latter-day Saints. The Catholics believe that they are the true church and that they have the Divine authority to act in the name of God because they trace their priesthood authority back to Peter, who they claim was the first Bishop of Rome. (Actually Peter was never a bishop, he was an apostle of the Lord Jesus Christ).
These churches, although they are man made organizations and not the true Church of Jesus Christ, nevertheless have many truths and do much good. Other than recognizing that they are not the official organization of God on the earth we recognize and understand that they are populated by righteous, believing people of good will–all of whom will be blessed by God for the goodness of their lives. The practice of all true principles results in the blessings of heaven on those who do good in the name of the Savior.
The Mormons believe that the Church of Jesus Christ of Latter-day Saints is the one true church because in the year 1820 both the Father and the Son appeared in person to the boy, Joseph Smith, and commissioned him to organize again the same Church had been organized by the Savior during his mortal sojourn, and had fallen into apostasy shortly after his death . Following that visitation the power and authority of the holy priesthood was restored to Joseph Smith and others by the laying on of hands of resurrected beings who held that authority in the time of the Savior. John the Baptist restored to Joseph Smith and Oliver Cowdery the priesthood of Aaron, with the authority to baptize for the remission of sins, and administer in all the offices of the Aaronic Priesthood. Later, the three apostles who presided over the church following the crucifixion of the Savior, Peter, James and John, appeared to Joseph Smith and Oliver Cowdery and restored to them the Melchizedek priesthood that has the authority to administer in all the spiritual and ecclesiastical offices and affairs of God’s kingdom on the earth. They were directed by the Lord to officially organize the Church on the sixth day of April, 1830, and were commanded to give it the name of the Church of Jesus Christ of Latter-day Saints–to distinguish it from the Church of Jesus Christ of the former day saints, the organization that existed in the time of the Savior.
Since the Church of Jesus Christ of Latter-day Saints is indeed God’s kingdom on the earth, anyone who is willing to ask God, in sincerity and with faith, if it is the one and only true church on the earth, the Holy Spirit will move upon that person, giving him an abiding assurance that indeed it is so. The following scripture declares this to be the case.
And when ye shall receive these things, I would exhort you that ye would ask God, the Eternal Father, in the name of Christ, if these things are not true; and if ye shall ask with a sincere heart, with real intent, having faith in Christ, he will manifest the truth of it unto you, by the power of the Holy Ghost. (Book of Mormon, Moroni 10:4)