Yamina Chairman Naftali Bennett met with Netanyahu challenger Yair Lapid, chairman of Yesh Atid Saturday evening, but gave no indication of progress toward an elusive resolution to Israel's political deadlock.
The meeting, which lasted two and a half hours, was described as "good" and an additional meeting will be held shortly, and came one day after his talks with Prime Minister Benjamin Netanyahu on Friday.
Lapid is expected to offer Bennett a rotation deal for the premiership, with Bennett serving first, if the Yamina leader recommends that Lapid be tasked with forming the government.
Yamina sources say that it is unlikely that Bennett will agree to the proposal.
Sources close to Bennett say he does not intend to recommend either Netanyahu or Lapid to the president. Instead, Yamina members will likely recommend that Bennett be given the mandate to form the government.
Meanwhile, Kahol Lavan chairman Benny Gantz declared on Saturday that "a disaster will befall us if an extreme right-wing government is formed" headed by Netanyahu, "without a balance that will protect the good of the citizens."
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As Bennett was set to meet Lapid on Saturday, many members of Yesh Atid are suspicious that he is using talks with anti-Netanyahu parties to apply pressure on and extract concessions from Netanyahu.
Netanyahu held a three-hour meeting with Bennett on Friday, as coalition talks continued following last week's election. Bennett, whose party won seven seats, has not committed to joining a coalition led by Netanyahu, nor has he ruled it out.
According to a statement from Yamina, the two politicians discussed "the need to form a stable and functioning government as soon as possible, and the options of making that happen in the current political situation."
Sources close to Netanyahu and Bennett have kept the content of the meeting under wraps, but the statement issued by Yamina appeared to hint that they believe the chances of forming a right-wing coalition have decreased after the announcement by Religious Zionism Chairman Bezalel Smotrich that he would refuse to join a government that includes the United Arab List.
The statement also did not repeat a point that Bennett has consistently made: that he would do everything possible to prevent another election from being called.
Ahead of the meeting, sources said Netanyahu was expected to offer integrating Yamina into Likud, reserving seven spots on Likud's election slate for Yamina lawmakers, and a number of ministerial portfolios, including naming Bennett defense minister.