The comments by Dallin H. Oaks and Russell M. Nelson came on the second and last day of the denomination's semiannual general conference, The Salt Lake Tribune reported Monday.
Oaks said declining birthrates, delayed marriages and rising numbers of people living together without marriage was creating pressure "to establish behaviors contrary to God's decrees."
While political and societal pressures had allowed for same-sex marriages in some states, Oaks said, "our policies are determined by the truths God has declared to be unchangeable."
"Marriage between a man and a woman is God's pattern for a fullness of life on Earth and in heaven," Nelson told the gathering. "God's marriage pattern cannot be abused, misunderstood or misconstrued."
Nelson and Oaks are recognized as "apostles" by church members.
A group of 130 people, mostly women, that promotes the ordination of women in the LDS church were turned away from the conference Saturday night.
Another apostle, Neil L. Andersen, explained that only men could be ministers in the church because "gender is an essential characteristic of both our mortal and eternal identity and purpose. Sacred responsibilities are given to each gender."