Livni, 50, once an agent of the Mossad spy agency, has pledged to pursue peace with the Palestinians and Syria, following up negotiations started by Prime Minister Ehud Olmert. She would be Israel's first female premier since 1974.
Even before President Shimon Peres gave her the official title of prime minister-designate on Monday evening, Livni was already conducting intensive talks with party leaders over their terms to join a coalition.
After Peres handed her the folder with the official appointment, she said, "I agree to take upon myself the role of forming a government," but only when Peres prompted her that she needed to accept the task.
In the minute-long ceremony at the president's residence, Livni, dressed formally in black and sitting in an armchair across from Peres, did not comment on policy issues.
Later the two read statements to reporters. Livni noted, "These are not normal days for Israel. There are great diplomatic and economic challenges facing it." She appealed to the parties in Olmert's government to continue in hers, and to other parties to join, including the hardline Likud, led by ex-premier Benjamin Netanyahu.
"The first priority that is right for Israel is a government that will serve to the end of the current term," in late 2010, she said.
Netanyahu has rejected the idea of a broad "national unity" government with Livni, preferring elections. Polls show he could win.
As leader of the largest party in the parliament, Livni was the automatic choice to succeed Olmert, who resigned Sunday because of a string of corruption allegations. Last week Livni won a primary election to replace Olmert as head of their Kadima Party, which has 29 seats in the parliament.
Peres compressed the allotted week of party consultations into less than a day an a half before appointing Livni. Peres was leaving later Monday for New York, where he is scheduled to address the U.N. General Assembly on Wednesday.
Olmert's coalition, which serves as a transition government until the parliament approves a new one, represents 64 out of the 120 seats in the parliament. Livni's most apparent option would be to recreate the same coalition of her Kadima Party, Defense Minister Ehud Barak's Labor, with 19 seats, the ultra-Orthodox Jewish Shas with 12 and the Pensioners Party with four.
But nothing is automatic in Israel's unruly political arena.
Shas or Labor may decide that their interests are better served in a snap election, though polls indicate that could be a dangerous choice, especially for Labor, which could lose strength.
If Livni fails to set up a coalition that can win parliamentary approval, Israel would hold an election within 90 days. Then the work of hammering together a coalition government would start over, stretching well into next year.
Olmert and Palestinian President Mahmoud Abbas pledged to try for a peace accord by January, though negotiations have yielded little apparent progress and both sides have said they were skeptical that the target could be met. Israel's political turmoil adds to the doubt.
Israel has also had several rounds of indirect peace talks with Syria, resuming contacts that were broken off in 2000.
Though Olmert has said he would pursue peace negotiations as long as he is prime minister, as an official lame duck, he is unlikely to be perceived as having enough clout to forge a peace agreement. An election campaign would probably freeze peace efforts for months.
By Associated Press Writer Mark Lavie