Mahmoud Abbas called Zehava Gal-On to offer condolences following the death of her father.
Peace Now secretary-general Avi Buskila the first Sephardi head of Peace Now.
Zandberg, 41, said she believes the time has come for Meretz to have young, new leadership after years of the press declaring the party tired, boring, and irrelevant.
Avi Dabush, whose parents were born in Libya and Syria, would bring a new identity to Meretz, which has never had a Sephardi leader.
The council approved the new procedures, with 87% voting in favor.
The party will hold a membership drive through February 17 that will allow thousands of new people to vote in the race.
Politicians from across the political spectrum came out against the United Nations vote.