The state central committee will vote on a June 19 decision where GOP officials agreed that Peterson is the party's leader for another two-year term.
Disputes over whether Peterson is still in charge have been in focus since the state Republican convention concluded weeks ago. Delegates failed to vote on a new state chair or elect any new party officer.
Peterson said in a news release Monday that the factions inside the party reminded him of the story of King Solomon. The Bible says the king settled a fight between two women over a baby by calling for the child to be split in half. "Only one showed a mother's love by offering to give up her child to save his life," Peterson wrote.
Peterson said he was preserving the party's integrity by calling the meeting rather than simply continuing as chairman without further discussion.
Establishment Republicans have accused Peterson of stacking committees to make sure far right conservatives continue serving in key GOP leadership positions.
Peterson and other tea party favorites have responded saying they're enforcing long-overlooked Idaho GOP rules.
Peterson did not return calls from The Associated Press.
Multiple opinions have been written offering conflicting arguments whether Peterson is still the party leader and whether he has the authority to call special meetings.
Most recently, an opinion from Twin Falls Republican and county prosecutor Grant Loebs made the case that Peterson's two-year term expired Monday.
A state rules panel, however, determined last week that Peterson was the state chairman because Republicans voted to adjourn knowing that they were selecting all standing party officers to serve another two-year term.
The state central committee will meet Aug. 9. The location has not yet been determined.