JERUSALEM, (Reuters) – Israeli Foreign Minister Tzipi Livni began talks on forming a new coalition government on Thursday after edging home in a party leadership contest that set her on course to replace Ehud Olmert as prime minister.

Among those she spoke with by telephone was U.S. Secretary of State Condoleezza Rice, who hopes Livni and Olmert can still clinch some form of peace deal with the Palestinians before the Bush administration quits the White House in just four months.

Palestinian negotiators welcomed her election in Wednesday’s poll, though they hold out little hope of a major breakthrough.

Livni, a lawyer and former Mossad agent, faces other battles — to stave off an early parliamentary election that she would probably lose and to build a multi-party cabinet on the remains of the fractious administration Olmert will leave behind when he finally steps down under the weight of a corruption inquiry.

Olmert is determined to go on handling talks with the Palestinians as caretaker premier until Livni forms a new team. The woman who would be Israel’s first female leader since the redoubtable Golda Meir in the 1970s said after her narrow win in the Kadima party ballot that her priority was “stability”.

Livni, 50, began what could be a weeks-long process of forging new coalition agreements by meeting two of the men she beat to the leadership of Kadima, a centrist party founded just three years ago by Ariel Sharon and which is the biggest group in a fragmented Israeli parliament with only 29 of 120 seats.

Analysts say that holding Kadima itself together could be as big a challenge as cutting deals with other coalition parties.

Media reports said that Mofaz cancelled a meeting with Livni scheduled for Friday.

Mofaz stunned her supporters overnight when a protracted count defied exit poll forecasts of a double-digit winning margin for the foreign minister.

In the end, hours after Livni had claimed victory, she was declared the winner by just 431 votes, or 1.1 points, with 43.1 percent of the vote. Two other candidates trailed well behind.

“The national mission … is to create stability quickly,” Livni said outside her Tel Aviv home at dawn. “On the level of government in Israel, we have to deal with difficult threats.”

To resist calls from right-wing opposition leader Benjamin Netanyahu for an early parliamentary election — which polls indicate Netanyahu’s Likud would win — Livni must persuade Defence Minister Ehud Barak to keep his Labour party in the coalition and do the same for the Jewish religious party, Shas. She met Barak at a routine security cabinet meeting on Thursday and later held talks with Shas leader Eli Yishai.

Though Barak allies have called for an election, Labour is wary of actually going to a vote, given Likud’s strength. Shas has made clear it wants assurances of welfare payments for its mostly poor, religious constituency as part of any deal.

Netanyahu, a hawkish prime minister a decade ago, told a news conference: “The cleanest thing, the responsible thing, the right thing and most democratic thing is to go to new elections. “We need to let the millions of Israeli citizens choose who will lead them and not … a few hundred Kadima voters.”

Allies said Livni was likely to pursue similar approaches to the Palestinians as under the Olmert government, though indirect talks with Syria may slow as Livni, who has been less involved in that process, waits for a new U.S. president in the new year. “We negotiate with whomever our neighbours choose, be it Livni or anyone else,” Palestinian President Mahmoud Abbas said.

Dubbed “Mrs Clean” in the media, the often dour foreign minister is seen by some as the antithesis of Olmert, a glad-handing veteran politician who hit trouble when an American businessman testified to giving him envelopes stuffed with cash. But the daughter of prominent Zionist guerrilla fighters of the 1940s will require combative spirit and political flair to live up to some supporters’ hopes she can be a new Golda Meir.

Commentators questioned whether her narrow victory in a vote among party activists gave her a mandate for tough decisions.

Mofaz’s campaign threatened to appeal but the Iranian-born former defence chief, popular among fellow Jews of Middle Eastern as opposed to European origin, finally accepted the result and said he planned now to take a break from politics.

Olmert will notify the cabinet on Sunday of his resignation, and must then go to Israel’s president, who will be travelling abroad, to formally resign, said Olmert’s spokesman, Mark Regev.