By Dan Williams

JERUSALEM, May 2 (Reuters) - Tzipi Livni is Israel's second woman foreign minister after the late Golda Meir. And many Israelis would like to see her, like Meir a generation ago, go on to become prime minister.

They may have that chance after the 48-year-old former Mossad spy, in typically dispassionate and soft-spoken tones, told a news conference on Wednesday she had just urged Prime Minister Ehud Olmert to resign and would seek leadership of his ruling Kadima party if he did.

"Now is the time to restore the public's trust in the government," Livni said, two days after a government-appointed inquiry commission savaged Olmert's conduct of last year's war against Hezbollah guerrillas in Lebanon.

Livni, whose father was a prominent guerrilla leader during Israel's founding struggles, has an electoral appeal based as much on what she isn't as on what she is -- especially when contrasted to the embattled Olmert. She is demure, even dour, in public, shying away from some of the traditionally bombastic rhetoric of Israeli leaders. Unlike Olmert and other top ministers, she has largely eluded scandals as well as domestic recrimination over the Lebanon war.

"There is a leadership crisis in Israel, and Livni is seen as the possible answer," said political analyst Amotz Asa-El.

"The modesty she evinces is an asset given the growing exasperation with a political establishment that is too macho in tone and often criminal in action."

LOYALTY

Livni had long pledged loyalty to Olmert, with whom she defected from the right-wing Likud Party with then Prime Minister Ariel Sharon, when he bolted to form the centrist Kadima in a bid to push through Israel's 2005 Gaza pullout.

But the Winograd inquiry into the war has triggered a major power struggle within Kadima, which sits at the centre of a coalition grouping some two thirds of parliamentary seats.

Polls see Livni easily succeeding Olmert as party head if he is forced to step down. Her approval ratings rival those of rightist opposition leader Benjamin Netanyahu, whose popularity has soared amid Israeli fears over Palestinian Hamas and Iran.

Like Olmert and Netanyahu, Livni hails from hard Zionist stock. Her father, Eitan, led an armed underground in the 1940s that fought for Jewish independence in all Palestine rather than for partitioning the territory with Arabs.

Livni renounced any such views after joining Sharon's cabinet as justice minister. "I came to the painful realisation that if I have to choose between a Greater Israel and Israel continuing to be a Jewish and democratic country, I must choose the latter," she said.

She came to politics just over a decade ago, following a stint in the Mossad intelligence service -- as a legal adviser, some say, while others speculate that she helped hunt Arab enemies abroad -- and then a career as a corporate attorney. Critics suggest that, as premier, she would have to work hard to make up for matters of state where she lacks expertise.

"Livni has proven herself in leadership situations," Asa-El said. "But that is not the same as proving herself as a leader."

She is married and has two children.

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