He urged church members to "keep on the covenant path", emphasizing the importance of the temple in the lives of church members.
Nelson is now considered a "prophet, seer and revelator" by Mormons.
Former LDS Church president Thomas S. Monson passed away January 2 at age 90 after more than six decades of service to the LDS Church.
The Church of Jesus Christ of Latter-day Saints has named its new president and prophet this week.
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"God loves his children and we love them and there's a place for everyone", Nelson said.
Oaks' approach to these issues also contrasts with that of Dieter F. Uchtdorf, who served in the First Presidency under Monson but was not chosen to continue in that role by Nelson.
As if to reinforce the point, Nelson appointed Dallin H. Oaks, 85, a member of the Quorum of the Twleve Apostles, as his first counselor on the First Presidency. Church presidents serve until they die.
Oaks took the lead late past year in defending the policy, telling a worldwide audience of Mormons: "Even as we must live with the marriage laws and other traditions of a declining world, those who strive for exaltation must make personal choices in family life according to the Lord's way whenever that differs from the world's way".
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Nelson's selection follows a longstanding succession plan that makes the longest-tenured member of the faith's Quorum the next church's president. "We need their voices, we need their input and we love their participation", Nelson said. He is the 17th man to hold the church's highest leadership position.
"We'll live to see the day when there will be other flavors in the mix, but we respond because we've been called by the lord", Nelson said.
The president and his two counselors are the members of the First Presidency, the highest governing body of the church.
"This is a great time is history of the church", Eyring said next.
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In April, the church is expected to fill the two vacancies, left from Monson's and previously Robert D. Hales' death in October.