Tzipi Livni has claimed victory in the contest to lead Israel's ruling Kadima party as exit polls suggest she won by a clear margin.
The foreign minister told supporters in a radio broadcast that "the good guys" had won after the ballot by members of the party.
Prime Minister Ehud Olmert is resigning amid corruption allegations.
If she can form a coalition Ms Livni, 50, would become Israel's first woman prime minister in more than 30 years.
Two television exit polls suggested Ms Livni had beaten Transport Minister Shaul Mofaz by a margin of 48% to 37%.
If the results are confirmed and there is a clear poll winner, the leader will have about six weeks to form a new coalition, during which time Mr Olmert will remain prime minister.
The scene in Tzipi Livni's campaign headquarters has been one of jubilation.
The foreign minister is regarded as being more dovish than Mr Mofaz, when it comes both to dealing with the Palestinians and possibly to her readiness to order military action against Iran, the BBC's Tim Franks reports.
Mr Olmert, Kadima's outgoing leader and the current prime minister, congratulated Ms Livni on her apparent victory, his office said in a statement.
In a conference call, Ms Livni thanked her supporters for their efforts and pledged not to let them down.
"You were just incredible," she said.
"And the good guys won... I just want afterwards not to disappoint any of you and to do all the right things that you fought for."
Critics say Ms Livni, a former Mossad spy, lacks political experience.
Shmuel Sandler, professor at the Begin-Sadat Centre for Strategic Studies, noted:
"[Ms Livni] is a good choice as far as Israel's foreign relations are concerned, but there is still the tension with Iran. I am not so sure how much experience she has for such matters and if she will be able to take the right decisions.
"She looks like 'Mrs Clean'... but she will still have to form a coalition," he told Reuters news agency.
"It is very difficult to predict whether she will be a strong prime minister."
Kadima was formed three years ago when former Prime Minister Ariel Sharon split from Likud to draw together support from left and right for his policy of unilateral withdrawals from the Gaza Strip and parts of the West Bank.
But its poll ratings fell as a stroke left Mr Sharon in a coma.
His successor, Mr Olmert, faced strong criticism of his handling of the 2006 Israel-Lebanon war and he was investigated in several corruption scandals.
Polls now suggest Likud could win a potential general election, which would take place if a coalition government cannot be formed in the wake of the Kadima leadership vote.
The Kadima election comes as the US government is continuing its push for an Israeli-Palestinian peace deal before President George W Bush leaves office in January.
Mr Olmert and Palestinian Authority President Mahmoud Abbas held talks on Tuesday and a spokesman for the outgoing prime minister said the two would continue to meet until a new government was sworn in.
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