Minutes before the news came out that the Likud leader would be asked to form a government, Ms Livni said what was being proposed was a government "without political vision, a government with no values".
"I will not be a pawn in a government that would be against our ideals," she said.
Israel's Haaretz newspaper reported on Thursday that Ms Livni said she would consider a coalition which included Likud, Kadima, and Yisrael Beiteinu.
She ruled out joining a coalition which included a number of other right-wing parties, the newspaper reported.
One of the main points of contention between the two parties is how to handle the Palestinian territories.
Ms Livni favours more talks and the creation of a separate state for the Palestinians.
Mr Netanyahu says he does not want Israel to rule the Palestinians, but says they should not be allowed things he considers a threat to Israeli security, such as an army, or control of airspace or the Jordan Valley.
Likud's 1999 charter "flatly rejects" a sovereign Palestinian state, but backs Palestinian self rule.
Palestinian officials reacted with caution to the news of Mr Netanyahu's appointment.
Saeb Erekat, a senior aide to Palestinian Authority President Mahmoud Abbas, who has been negotiating with Israel's outgoing Kadima-led coalition, said Israel needed a government committed to peace.
"We will not be in the negotiations with an Israeli government that continues settlement activities, that refuses the two-state solution, and that doesn't accept agreements signed," he said.
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