Yamina party chairman Naftali Bennett and United Arab List chairman Mansour Abbas met Wednesday morning to discuss the "current political climate" and explore options for establishing a government.
Meeting at the Knesset, the two leaders said the meeting "went well."
A number of parties that form the the 'anti-Netanyahu' bloc, Yesh Atid, Yamina and Tikva Hadasha, have been discussing coalition plans with "positive energy" in recent weeks.
"All sides are interested in such a government, and they both want to demonstrate flexibility to make it happen. But it's clear that there's ideological differences that will be hard to bridge," a source close to the negotiations told Haaretz.
It is understood by the political system that Prime Minister Benjamin Netanyahu knows that he won't be able to form a coalition, and is now focusing on thwarting his opponents' attempts.
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In recent days, Netanyahu has offered several leaders a rotation deal for the preimership. Yet political sources told Haaretz that Netanyahu knows these offers are unlikely to end in a coalition agreement.
On Friday, Bennett said he has "begun the effort to form a right-wing unity government," after realizing Prime Minister Benjamin Netanyahu wasn't going to reach agreements with other parties to form a right-wing government.
In another blow to the prime minister, the anti-Netanyahu bloc won a key vote to determine the composition of the Knesset arrangements committee last week.
The committee is responsible for setting the Knesset agenda during the transitional period between an election and the formation of a new government. This means that the committee controls which bills come before the Knesset for a vote during this time, giving the committee's extraordinary influence.