The group signingforsomething.org disagrees with The Church of Jesus Christ of Latter-day Saints' support for California's Proposition 8, which would ban same-sex marriage in the state's constitution.
"I think it's important that the leadership of the church knows that we have varying opinions within the church and that we're not all in lockstep behind them," said Andrew Callahan, a local church leader from Hastings, Neb., and a member of the group.
Callahan and others started signingforsomething.org after a June call from leaders of the church asking members to give time and money to help pass the proposition, which will be on the Nov. 4 ballot.
The proposition would overturn the California court ruling that legalized gay marriage. The Mormon church is part of a coalition of faiths and conservative groups working to pass the proposition.
A message seeking comment from the church was not immediately returned Thursday.
Callahan said church members worldwide have posted letters on the Web site and signed the petition. He plans to deliver the materials on Friday.
"The letters are mostly from the U.S. and Canada, but we have letters from China, from Taiwan, England and Australia," he said. "I'm not sure they are going to let us drop them off. I wouldn't be surprised if they tried to have security meet us at the door."
The petition asks church leaders to "stop political organizing efforts and financial support of attempts to use government to restrict the secular and religious rights of gay and lesbian individuals." It also asks the church to retract its request that members support such measures.
The petition's authors said the church is forcing the morality of the Mormon belief system on others and that is contrary to church doctrines that say it is not just to "mingle religious influence with civil government."