The general election in Israel has returned a hung parliament, with just one seat separating the main right and left wing parties in the Knesset.
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.
Negotiations
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.
Serious concern
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.