Israel's President Shimon Peres asked Foreign Minister Tzipi Livni on Monday to form a new government, a day after scandal-plagued Prime Minister Ehud Olmert officially stepped down.

Livni, 50, a former Mossad spy who replaced Olmert as head of the centrist Kadima party in a leadership vote on Wednesday, is hoping to become Israel's second woman prime minister after Golda Meir, who served from 1969 to 1974.

"After consultations with the political parties, the president has asked Kadima party leader Tzipi Livni to form a government", public radio quoted an official statement as saying.

Livni now has 42 days to form a governing coalition in order to avert snap elections that polls indicate would bring the right-wing Likud party of former prime minister Benjamin Netanyahu to power.

Traditionally, the task of forming a government goes to the party with the most seats in the Knesset, in this case Kadima, which has 29 MPs in the 120-member parliament.

Livni has already begun talks with parliamentary factions that could be included in a future coalition, while at the same time pressing members of her own party to close ranks.

But in the rough and tumble of shifting allegiances in Israeli politics, there is no guarantee that she will be able to come up with the numbers to form a coalition government and thus avoid an early election.

The Labour party, the main partner in the current coalition, has sent mixed signals, having met Netanyahu over weekend and called for either early elections or a "national emergency government." Livni met Labour chief Defence Minister Ehud Barak hours after Olmert formally submitted his resignation and offered to make the party a "full partner" in a new coalition, according to Haaretz newspaper, quoting unnamed Livni aides.

Meanwhile the ultra-Orthodox party Shas - which has frequently played the kingmaker - has vowed to leave any government that negotiates the future of Jerusalem, a key issue in efforts to reach a peace deal with the Palestinians.

Livni also faces tough challenges in seeking to unify Kadima after new rifts emerged in the wake of her narrow victory over transport minister and former army chief Shaul Mofaz.

Formed less than three years ago, the centrist party has itself been dogged by allegations of corruption.

Olmert's decision to resign after just 32 months in office followed months of pressure from supporters and rivals alike in the face of a string of graft allegations against him.

Police have recommended criminal charges against the 62-year-old Olmert in two cases in which he is accused of accepting large sums in cash from a US financier and multiple-billing foreign trips.

He has denied any wrongdoing.

The continuing political turmoil has cast a shadow over Israeli peace talks with the Palestinians which were revived only in November, further denting hopes of a deal by the end of this year.

Both sides remain deeply divided on core issues, including final borders, Jewish settlements in the West Bank, the fate of 4.6 million Palestinian refugees and the future status of Jerusalem.

Shas's refusal to negotiate the fate of Jerusalem could prove particularly tough for Livni, who is currently the lead negotiator for Israel.

The Palestinians want mostly Arab east Jerusalem, which Israel occupied in the 1967 Six Day War, as the capital of their future state.

Israel, however, considers the entire city to be its "eternal, undivided" capital, a claim not recognised by the international community.