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The indecisive result gave the governing Likud party 40 seats, while the centrist Labour Alignment won 39 seats. Both parties lost seats in the election.
A similar result in the last general election in 1984 led to a power-sharing coalition between Likud and Labour, led by Shimon Peres.
Under the coalition, Mr Peres served as prime minister from 1984-1986, with Mr Shamir taking office for the last two years.
But the alliance has always been an uneasy one, as the two party leaders have radically different ideas.
Mr Shamir opposes any land-for-peace deal, and refuses to negotiate with the Palestine Liberation Organisation.
Mr Peres, who served as foreign minister during the Shamir government, strongly supports the US initiative for an international conference on peace in the Middle East, currently stalled and likely to be abandoned after today's election result.
Both parties are now saying they want the coalition to end.
Likud is engaged in feverish negotiations to form a government with the help of ultra-orthodox right-wing religious parties, which did better than expected and won 18 seats - an increase of six seats on their previous showing.
If Mr Shamir can do a deal with the religious right, he would have a majority in parliament which would allow him to form a government led by Likud, without the need to include Labour.
Several of the ultra-orthodox religious parties favour a policy of expelling Palestinians from the Israeli-occupied West Bank and Gaza Strip.
The re-emergence of the religious parties as key players in Israeli politics has caused serious concern among Israel's secular majority.
There have been several calls to change the country's electoral system, which relies on an extreme form of proportional representation but has failed to produce a majority government for two successive elections.
Palestinians in the occupied territories reacted to the prospect of a Likud-led government with dismay.
The Palestinian uprising, the Intifada, began almost a year ago, and there were further disturbances in the occupied territories today in which an Arab youth was killed.
Despite nearly two weeks of negotiations, deep divisions within the ultra-orthodox parties dashed Yitzhak Shamir's hopes of forming a government without Labour.
By the end of the month, another national unity government had been formed, with Likud at the head and Labour occupying key cabinet positions.
In 1990, the coalition government lost a no-confidence vote.
When Labour could not find enough allies to enable it to continue, Shamir returned to power and led a Likud government in alliance with extreme right-wing and religious parties.
Under his rule, Jewish settlements in occupied territories were expanded, and the UN-sponsored Middle-East peace conference in 1991 became deadlocked under Shamir's implacable opposition to a land-for-peace deal or Palestinian self-determination.
Shamir was defeated in the 1992 election and the Labour Party returned to power. In 1993 he left the Likud Party leadership.
In retirement, he urged the scrapping of the Oslo accords with the PLO in 1993.
Likud returned to power under Prime Minister Ariel Sharon in 2001, and was re-elected in 2003.
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