* Netanyahu's Likud secures far-right ally

* Peres to seek Likud-Kadima unity government

* Kadima rejects Likud alliance

(Adds Peres to press for unity government)

By Jeffrey Heller and Ori Lewis

JERUSALEM, Feb 19 (Reuters) - Benjamin Netanyahu's chances of becoming Israel's prime minister again were boosted on Thursday by the conditional backing of an ultra-nationalist politician who emerged as a kingmaker in a close election.

Avigdor Lieberman, leader of the Yisrael Beiteinu party, recommended to Peres that he choose Netanyahu to form a government, if the right-wing Likud chief pursued a broad coalition. Netanyahu has said he would do so.

President Shimon Peres plans to ask Netanyahu and rival Tzipi Livni of the centrist Kadima party on Friday to join forces to form a unity government, a presidential official said.

Livni and Netanyahu both laid claim to the premiership after Kadima won 28 seats in the 120-member parliament to Likud's 27 in an inconclusive Feb. 10 election that deepened uncertainty about peace moves with the Palestinians.

Netanyahu renewed calls on Livni and Labour Party leader Ehud Barak to join a coalition under his leadership. Livni rejected his call, saying her party will sit in the opposition. Labour has said it will do the same.

"I don't intend to be a fig leaf for a government that has no path and is dysfunctional. I don't intend to change my path or to betray the voters for a job in the government," Livni said before meeting a visiting U.S. congressional delegation.

Peres wrapped up consultations with party leaders and would meet Netanyahu and Livni separately on Friday.

Netanyahu served as prime minister from 1996 to 1999. During his term he handed over part of the West Bank city of Hebron to the Palestinians.

With Lieberman's support, Netanyahu has the backing of some 65 legislators, enough for a narrow, governing majority of right-wing and Jewish religious parties.

UNITY

Lieberman, an immigrant from the former Soviet Union who has been at odds with religious parties and is reviled by Israel's Arab community, made unity the theme of his remarks to Peres.

"We recommend Benjamin Netanyahu, only in the framework of a broad government," Lieberman told reporters.

"We want a government of the three biggest parties, Likud, Kadima and Yisrael Beiteinu," he said, without disclosing what he would do if a unity government proved impossible to achieve.

A Yisrael Beiteinu official said Lieberman sought a broad coalition out of concern that creation of a narrow, rightist government could lead to friction with the Obama administration, which has pledged to pursue Palestinian statehood.

Kadima has said it would be willing to relinquish parts of the occupied West Bank in exchange for peace, a position that would put it in conflict with Yisrael Beiteinu and Likud.

Yisrael Beiteinu, which won 15 seats in last week's ballot, has angered Israel's Arab citizens by proposing a law under which Israelis would have to pledge allegiance to the Jewish state as a condition for voting or holding office.

The party also wants to trade land inside Israel in which many of the country's 1.5 million Arabs live for Jewish West Bank settlements in any peace deal with the Palestinians.

Under Israeli law, the legislator designated by Peres to try to form a government has 42 days to complete the task. Traditionally, after an election, past presidents have picked the leader of the party that won the most votes, but there is no legal obligation to do so. (Additional reporting by Joseph Nasr and Allyn Fisher-Ilan, Writing by Jeffrey Heller; Editing by Angus MacSwan) (For blogs and links on Israeli politics and other Israeli and Palestinian news, go to http://blogs.reuters.com/axismundi)

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