The group quotes Mormon founder Joseph Smith, saying he hoped to make the all-woman Relief Society "a Kingdom of Priests," and sees female ordination as realizing that vision.
This priesthood push is "an act of faith," said Kate Kelly, an international human rights lawyer in Washington, D.C., and one of Ordain Women's founders, "faith that the church can change, faith that our efforts will be respectfully received, and faith that others will join us."
The LDS Church responded by emphasizing that God loves both genders equally.
"The worth of a human soul is not defined by a set of duties or responsibilities," spokeswoman Jessica Moody said in a statement Tuesday. "In God's plan for his children, both women and men have the same access to the guidance of his spirit, to personal revelation, faith and repentance, to grace and the atonement of his son, Jesus Christ, and are received equally as they approach him in prayer."
But a male-only priesthood "was established by Jesus Christ himself," Moody said, "and is not a decision to be made by those on Earth."
That's precisely why Kelly, a lifelong Mormon who served an LDS mission to Barcelona, Spain, married in the Salt Lake Temple and a devout member, hopes church leaders seek divine guidance on the question.
And she is not alone.
Kelly has been "surprised by the extremely broad swath of people who have responded," she said in a phone interview, "and pleasantly shocked by how excited people are about this."
Though the number of Ordain Women profiles is relatively small about two dozen so far the 2-week-old website has garnered more than 100,000 page views, Kelly said, and her local LDS leaders, male and female, have been supportive of her.
"We sustain the prophet and the Quorum of Twelve Apostles and ask them to prayerfully consider this change," she said. "We believe that what we are doing demonstrates our faith in the gospel."
Opening up the priesthood "would change the way Mormon women see themselves and live their lives," Kelly said. "It would be a way they can invest in and improve the church as an institution."
Besides that, she views female ordination as helping the church hold on to its young women.
Kelly points to a 2011 self-reported survey of about 3,000 Mormons who no longer believe in the church that found 63 percent of all women and 70 percent of single women cited gender issues as being the primary reason for their loss of faith.
Ordaining women could be, Kelly said, "a retention effort."
She and others will be on hand Saturday, the 183rd anniversary of the founding of The Church of Jesus Christ of Latter-day Saints, to officially launch Ordain Women. The6 p.m. meeting at the University of Utah will take place at the same time Mormon men and boys will be attending the priesthood session of the faith's General Conference.
This pitch for priesthood follows other activist drives to allow women to wear pants to church and to offer prayers in LDS General Conference.
However, priesthood ordination may not be a desired goal for most Mormon women.
In a survey of U.S. religion, authors Robert Putnam and David Campbell, in their 2010 book, American Grace: How Religion Divides and Unites Us, found that 90 percent of LDS women opposed female ordination in their church (ironically, only 52 percent of Mormon men were against it).
Even Mormon feminists appear divided on the issue.
"I love the grass-roots attitude that we can take our experiences into our own hands and shape them," said Neylan McBaine, founder of The Mormon Women Project, which showcases diverse, talented and strong LDS women. "But this particular movement [Ordain Women] doesn't resonate with me. My philosophies apply to local and individual levels. I am uncomfortable with movements that take on the church as a whole because I'm afraid that by overreaching we have no influence at all."
Last summer, McBaine, a creative director at Bonneville Communications, offered a list of potential changes short of ordination that would enhance the spirituality and visibility of women and girls in LDS services and programs.
Some have suggested, for instance, that women could serve as witnesses at baptisms, hold their babies during naming blessings or conduct young women's worthiness interviews.
The LDS Church has "a rich doctrine around priesthood that has yet to be explored," she said. "We could spend more time finding the nuances in priesthood that would allow us to maximize what we have rather than jumping to this panacea so quickly."
Activists should change the message, she advised, from " 'Let us have the priesthood' to 'We are capable of doing more. What else can we do to help?' "
The blog Feminist Mormon Housewives hosted an online discussion about women's ordination and the comments ranged from strongly in favor to unsure and opposed.
Sheri Dew, president of LDS Church-owned Deseret Book and a former counselor in the faith's General Relief Society presidency, has said in recent speeches how empowered she and other Mormon women are without the priesthood.
"We pray in public meetings, we speak, we expound scripture, we teach the doctrine ... we lead organizations," Dew said in a November 2012 "Time Out for Women" presentation posted on YouTube. "We teach the gospel on proselytizing missions. ... Women participate in ordinances that are decidedly of a priestly character in the House of the Lord [Mormon temples]. Nothing is held back from us."
Mormon women, Dew said, "get everything that our Father [in Heaven] is willing to give those who qualify to be joint heirs with his Son."
LDS General Conference is Saturday and Sunday at the Conference Center in downtown Salt Lake City. Saturday's sessions are at 10 a.m. and 2 p.m. with a priesthood meeting for male members at 6 p.m. Sunday's sessions are at 10 a.m. and 2 p.m.
The Ordain Women group, seeking to open up the faith's all-male priesthood to female Mormons, plans to officially launch its effort Saturday at the University of Utah's Union Building theater from 6 to 8 p.m. during the LDS priesthood meeting.