Foreign Minister Tzipi Livni accepted the task of forming a new Israeli government on Monday following the resignation of Prime Minister Ehud Olmert and called on her right-wing opponents to join a unity coalition.

There was no indication, however, that Benjamin Netanyahu, the former premier who leads the opposition Likud party, would drop his demand for an early parliamentary election instead -- an election which opinion polls suggest he could win with ease.

Livni was elected last week to succeed Olmert as leader of the centrist Kadima party, after he agreed to quit over a corruption scandal. Olmert tendered his resignation as premier on Sunday and, after consulting party leaders, President Shimon Peres asked Livni on Monday to form a new government.

She faces a daunting struggle, however, to build a workable parliamentary majority from among the 13 parties represented in the Knesset -- and until she does Olmert will remain in office as a caretaker, pursuing peace talks with the Palestinians.

If Livni, a 50-year-old commercial lawyer who once worked for the Mossad spy agency, cannot win parliamentary approval for a cabinet within six weeks, Peres could turn to someone else. The more likely outcome of her failure would be an immediate election, well before the next vote is due in 2010.

"My priorities are to try and form a national unity government and maintain the present coalition," she said. "Otherwise I will lead the Knesset to new elections as soon as possible."

If Livni succeeds, she will become Israel's first woman prime minister since Golda Meir in the 1970s.

NEGOTIATIONS

Livni has been in consultations across the spectrum, notably with Labour party leader Ehud Barak, whose leftist party is the second biggest in the outgoing government, and with the Jewish religious parties which always play a key role in coalitions.

Defence Minister Barak, himself a former prime minister, has made no secret of his own ambitions to reprise that role, though his lack of a seat in the present parliament and Labour's poor showing in opinion polls present him with major obstacles.

Barak has met Netanyahu since Livni took over the leadership of Kadima, a party formed only three years ago by rebels from Likud and Labour and which has only a quarter of Knesset seats.

Neither man was clear on what they discussed, though there has been speculation the two men, both former prime ministers and army commando officers, might try to thwart Livni's ascent.

Livni's very public gesture toward Netanyahu at a news conference with Peres immediately after her nomination, was seen by some Israeli commentators as a signal to Barak that he should not take for granted his own role in any coalition she forms.

"I call on the leader of the Likud party, Benjamin Netanyahu, to join a unity government led by myself in order to deal with issues which he knows face us with urgency," she said.

Aides to Netanyahu declined immediate comment.

Barak has said he wants a broad-based government that would include left- and right-wing parties: "What Israel really needs for the challenges it faces is a national emergency government."

The political uncertainty has dimmed even further prospects of an Israeli-Palestinian peace deal, which the United States had hoped Olmert and Palestinian President Mahmoud Abbas could achieve this year before President George W. Bush leaves office.

Livni has been chief negotiator with the Palestinians for the past year. Her Palestinian counterpart Ahmed Qurie said after she agreed to form a government: "We hope it will pursue peace talks seriously."

However, the immediate prospects for a deal on creating a Palestinian state seem poor. A return to power of the hawkish Netanyahu would be unlikely to improve them.