Monson, opening the Mormons' 183rd semiannual conference, said the number of missionaries has grown 37 percent since the church lowered the minimum age a year ago, The Salt Lake Tribune reported.
There are 80,333 missionaries in 2013, up from 58,500 in 2012.
The age for serving as missionaries was reduced last year from 19 to 18 for men and 21 to 19 for women.
Monson addressed 20,000 people gathered at the Salt Lake City Conference Center and millions more listening via telecasts and Internet streaming.
"Now is the time for members and missionaries to come together, to work together, to labor in the Lord's vineyard to bring souls unto him," Monson said. "He has prepared the means for us to share the gospel in a multitude of ways, and he will assist us in our labors if we will act in faith to fulfill his work."
Monson, 86, has served as president since 2008. He is considered a "prophet, seer, and revelator" by members of the church.