By Dan Williams and Jeffrey Heller

JERUSALEM, Feb 11 (Reuters) - Israel faced on Wednesday what could be weeks of political uncertainty after an election that ended with clashing claims of victory by centrist Foreign Minister Tzipi Livni and hawkish rival Benjamin Netanyahu.

With nearly complete final results giving Livni's Kadima party a slim edge of one or two seats over Netanyahu's right-wing Likud in the 120-member parliament, she pledged to lead a new government and invited him to join.

Netanyahu, pointing to what he called a large "nationalist camp" in parliament, said he would become prime minister and establish a governing coalition with rightist parties.

"With God's help I will lead the next government," Netanyahu, 59, told Likud supporters after exit polls on Tuesday gave Kadima a slim lead and right-wing parties some 64 parliamentary seats.

Addressing cheering Kadima activists, Livni, 50, said: "The Israeli public can smile again when we form the government." She would become Israel's first woman prime minister since Golda Meir governed in the 1970s.

It will be up to President Shimon Peres to decide, after hearing recommendations from political parties, whether to ask Livni, a relative newcomer to politics, or Netanyahu, a former prime minister, to try to put together an administration.

The overall rightward shift in the Knesset will, in any case, dent hopes in U.S. President Barack Obama's administration for an Israeli coalition that can move towards peace with the Palestinians and other Arab neighbours after last month's war in the Gaza Strip.

Peres's discussions with Knesset factions could take about a week and subsequent coalition negotiations could drag on for more than a month.

Ehud Olmert of Kadima, who resigned in September in a corruption scandal but stayed on as caretaker prime minister, will remain in the post until a government is in place.

Olmert will oversee processes such as the consolidation of a truce that ended the recent Gaza war against Hamas militants and preparations for any showdown over Iran's nuclear programme.

Whoever Peres chooses will have up to 42 days to try to put together a government. Israel's president traditionally picks the leader of the party that wins the most votes, but he is not legally bound to do so.

FAR-RIGHT KINGMAKER

Avigdor Lieberman, whose far-right Yisrael Beiteinu party, surged into third place on its anti-Arab rhetoric, emerged as a potential kingmaker.

He said he was leaving his options open, indicating he could choose to join a Likud or a Kadima-led government.

Defence Minister Ehud Barak's long-dominant, centre-left Labour party was cut down to fourth place behind Kadima, Likud and Yisrael Beiteinu, an upstart ultranationalist party catering mainly to immigrants from the former Soviet Union.

Netanyahu was cruising to victory until Olmert's centre-left coalition launched a three-week offensive in Gaza. It won massive popular support in Israel despite international outcry over the 1,300 Palestinians killed in the Hamas-ruled enclave.

Some political analysts said Netanyahu had been too complacent, enabling Kadima to catch up and Livni, a former Mossad spy and corporate lawyer, to gain in popularity.

Livni led peace talks with the Palestinians on a two-state solution, which stalled last year but which U.S. President Barack Obama wants to resume. Netanyahu is cooler on ceding occupied territory to Palestinians and is more likely to resist U.S. demands to curb settlement expansion in the West Bank.

During his three years in office to 1999, the U.S.-educated Netanyahu had strained relations with the last Democratic president, Bill Clinton, and Washington analysts believe a Livni administration would be favoured by the White House. However, her hands would still be tied by right-wing parties.

Though accustomed to breakneck electoral successions thanks to a fragmented parliamentary systems, even veteran Israeli observers were flummoxed by the Livni-Netanyahu impasse.

"This has, without a doubt, been one of the strangest election nights we have known," said Yaacov Elon, news anchor for Israel's Channel Ten television. (Additional reporting by Adam Entous, Joseph Nasr, Ori Lewis, Alastair Macdonald, Jeffrey Heller, Steven Scheer and Douglas Hamilton in Jerusalem, Wafa Amr in Ramallah and Tova Cohen in Tel Aviv, in Jerusalem, Editing by Michael Roddy) (dan.williams@reuters.com; +972 2 632 2202; Reuters Messaging: dan.williams.reuters.com@reuters.net)) (For blogs and links on Israeli politics and other Israeli and Palestinian news, go to http://blogs.reuters.com/axismundi)

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