Kadima leader Tzipi Livni's party rival, MK Shaul Mofaz, should lead the group of six Kadima rebels out of the party and into the coalition if she does not accept his demand to advance the party's next leadership race, one of the MKs told Mofaz on Tuesday. Sources among the rebels confirmed a Channel 10 report on Tuesday night that MKs in the group were demanding that Mofaz become their leader, and had even urged Likud leaders to pressure Mofaz to bring about a split in Kadima. They said they realized that one of the reasons the split did not happen last week was that they did not have a leader. Support for Mofaz's request to advance the race grew on Tuesday when MK Avi Dichter said that "everyone understands that there will be primaries in Kadima in 2010." Just two weeks ago, Dichter said the race should be a year before the next general election, which is currently set for November 2013. Kadima rebel MK Otniel Schneller tried to reach a compromise between Mofaz and Livni in Monday's stormy Kadima faction meeting. He said the primary should be held on June 3, so the campaign would take place while the Knesset is recessed and Kadima's parliamentary work would not be harmed. "My compromise was intended to keep Kadima intact," Schneller said. "Many people in the faction realize the primary must be held soon in order to finish the saga we are in and to put an end to our current shame. Every leader must make the decisions incumbent on them." Sources close to Livni said Kadima rebel MKs had told her that they opposed Mofaz's call to hold the primary within the next three months. Livni's associates said they did not believe the rebels were or ever will be an organized group, and that talk of a split in the party has ended. Mofaz's spokespeople downplayed the reports and said that Mofaz has made clear that he does not intend to split Kadima. They said Mofaz told the rebel MKs that he was not interested in leading a split and he only wanted to lead Kadima. In a press conference on Monday, Mofaz revealed that he told Livni that he would sign a promise to remain in the party if he lost the race if she would sign it too. A source close to Mofaz downplayed the good atmosphere at Monday night's festive Kadima dinner. They said the meal was "aspirin for a party that needs surgery that only primaries could provide."