Benny Gantz's Kahol Lavan party sent a letter to Knesset Speaker Yuli Edelstein of Likud on Friday, requesting to hold a vote for a new Knesset speaker on Monday.
Replacing Edelstein could let the party push through legislation to prevent Netanyahu from forming a government while under indictment.
This comes after Gantz and Netanyahu spoke overnight on Friday about the possibility of forming a unity government in light of the coronavirus crisis.
Before their meeting, Gantz said he is willing to discuss the formation of unity government that includes "all parts of the house," which would also include the Arab-majority Joint List, the third largest party in the Knesset.
Netanyahu later responded by saying there would be "no terror supporters" in the Israeli government.
A Kahol Lavan official said Friday that "Netanyahu is not serious about contacts with the emergency unity government. We asked him to send a negotiating team and start discussing with us, but in the meantime, that didn't happen. Therefore, we continue to conduct 'business as usual' in the event that the emergency government does not eventually arise, and we continue to act in order to replace Edelstein."
The official added that "If an emergency government emerges, the decision on the matter of the Knesset Speaker will be part of the coalition negotiations."
- Gantz: Ready to discuss forming unity gov't with Netanyahu amid coronavirus crisis
- Netanyahu says 'no terror supporters' in gov't after Gantz calls for unity with 'all parts of house'
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Gantz later wrote on Facebook that "So far I have not gotten a serious reply to my offer" from Netanyahu.
Likud slammed Kahol Lavan in a statement, saying it was dealing in small politics during a time of crisis.
Recently, Kahol Lavan has been trying to raise a majority in the Knesset for a minority government with the support of the Arab-majority Joint List, but has decided to change direction after realizing that this will not succeed.
During Netanyahu's talk with Gantz Friday, the party leaders announced they would meet soon upon Netanyahu's invite to discuss forming an emergency government to deal with the worsening spread of the virus.
Gantz said in response that In light of the situation, "we would be willing to discuss establishing a national emergency government that would include representation of all parts of the house." Netanyahu, for his part, said that "terror supporters" cannot be part of said government, neither in normal circumstances nor in emergency."