The conference call, titled "free the delegates," was led by Kendal Unruh, a Colorado delegate and a member of the GOP's rules committee, which shapes the rules of the convention. Unruh, who is pledged to Ted Cruz, wants to create a rule enabling delegates to abstain from voting for Trump, even if they are bound to him, if they feel it violates their moral or religious beliefs.
According to participants, there were approximately 30 people representing 15 states on the nearly hour-long phone call. According to one call participant, the focus was on coordinating the multi-state effort, and less on the official plan of action, which is in the works. News of the call was first reported by the Washington Post. Another phone call is scheduled for Sunday night.
"This call will introduce us to each other in preparation for an open “national leadership” call in a few days," the invitation, a copy of which was obtained by ABC News, explains.
Out of the conference call came a centralized method of managing the data, and talks to create a website explaining the mission, Unruh said.
The idea is to coalesce behind a plan to stop Trump and not unite behind a particular person, though many are former Cruz supporters.
Even if Unruh has managed to develop grassroots support for this idea, however, it is still an uphill climb for this to actually happen.
A conscience clause can only be implemented if it is approved by a majority of the rules committee. And even if the rules committee approves it, it still needs to be approved by a majority of the delegates on the convention floor.
According to current rules, delegates are bound to vote for the candidate they are pledged to -- which is based on primary and caucus votes. Trump has garnered 1,543 delegates, according to ABC News' most recent estimate, more than the 1,237 needed to clinch the nomination outright.
Also under current rules, if a candidate does not receive more than half of the delegates on the first ballot, some are released on the second ballot to vote for whomever they want.
Efforts to stop Trump have focused on fomenting dissent among delegates pledged to the real estate mogul or putting delegates in place who would not vote for Trump on subsequent ballots.
“Donald Trump won it fair and square,” Cindy Costa, a delegate from South Carolina who is also serving on the rules committee, said last week. An unbinding rule is not only unrealistic and unfair, she said, but would cause “magnificent chaos.”
Kelly Arnold, chairman of the Kansas Republican Party and another member of the rules committee, told ABC News last week he is going to do “what’s in the best interest” of the GOP.
"I don’t see myself making any drastic changes," he said.
Trump released a statement calling the effort “totally illegal.”
The RNC did not immediately respond to a request for comment.
ABC News’ John Kruzel contributed reporting.