President Reuven Rivlin urged on Blue and White leader Benny Gantz and Prime Minister Benjamin Netanyahu on Wednesday to find common ground that would end the year-long paralysis by reaching some sort of power-sharing deal.
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The president is responsible for choosing the prime minister-designate he thinks has the best chance of forming a stable government.
Upon officially receiving the results of last week's vote, Rivlin said he was open to any proposal brought forward but made a point to suggest that his framework from the previous round of failed negotiations was still relevant.
Rivlin, who will begin formal consultations with party leaders next week, took an active role in the previous round of talks and urged Netanyahu's Likud party and challenger Gantz's Blue and White party to join together in a unity government.
"I am certainly aware of the criticism of the outline that I presented then, and agree with much of it. But I did not believe there was another way and, even today, the situation has not changed a great deal," he said in a statement after receiving the results.
After a brutal campaign in which the two camps hammered each other with personal attacks on the other side's leader, a unity government would appear out of the question this time around. The attacks on Gantz have been so severe that his personal security has been increased because of viable death threats.
But both sides appear to be running into major trouble forming a government without the other.
Netanyahu and his religious allies only secured 58 of the 120 seats in parliament, leaving them three seats short of being able to build a coalition government.
His opponents control a parliamentary majority and are committed to ousting Netanyahu, who heads to trial next week to face corruption charges. However, Netanyahu's foes are deeply divided ideologically: Yisrael Beytenu and the Joint Arab List, two factions that are crucial if Gantz is to form a government, can't agree on anything.
Gantz met with the Joint Arab List's representatives on Wednesday, hoping to secure their indirect support for swearing in a government in a confidence vote next week.
But it appears that even if he gets them on board, his own ally, the Labor-Meretz-Gesher faction, may frustrate his plans.
On Tuesday, Gesher head Orly Levy-Abekasis said she would not back Gantz's government if it relied on support from the Arab parties. If she follows through on that threat, and if Gantz's two renegades at Blue and White don't support his move, he is unlikely to get a successful confidence vote passed for his proposed government.
Likud, which is banking on such a scenario, has already approached Labor leader Amir Peretz, prodding him to join a Netanyahu-led government.
Israel Hayom has learned that senior Likud officials have been pressuring Peretz and telling him that Blue and White are only using him for the purpose of preventing Netanyahu from getting a fifth government sworn in.
The officials warned him that Blue and White will ultimately join Netanyahu and form a unity government. When that happens, "Blue and White will throw you under the bus" and he will essentially have zero political clout, they have communicated.
They further said that in such a scenario, he would at best get an unimportant portfolio in the new Netanyahu government or the chairmanship of a Knesset committee.