Senior members of Israel's Kadima and Likud parties, which finished nearly even in Tuesday's general election, rejected the idea of a rotating premiership.
While Kadima won one more seat than Likud (28-27) in the next Knesset, overall the right-wing bloc ended much stronger than Livni's allied parties on the left (65-44), leaving much confusion over whom President Shimon Peres should choose to form the next government.
Israel solved a similar situation following the 1984 general election by forming a unity coalition between Likud and Labor that saw Yitzhak Shamir and then-Labor leader Peres serve two years each as prime minister.
But senior Kadima lawmaker Meir Sheetrit told Army Radio on Wednesday that such a solution today would be a gimmick at the expense of the Israeli public, and is rejected by his party.
Silvan Shalom, number 2 on the Likud list, told Army Radio that his party also sees no need for a power-sharing government, since such solutions are only called for when there is an equal balance between right and left, and Tuesday's election clearly put the right-wing on top.