Israeli Foreign Minister Tzipi Livni is beginning the task of putting together a new government after her election as leader of the ruling Kadima party.
She has 42 days to form a coalition and replace Ehud Olmert as prime minister.
The leadership vote was called after Mr Olmert, who will remain as caretaker prime minister, announced he would step down to fight corruption allegations.
Ms Livni narrowly beat Transport Minister Shaul Mofaz by just 431 votes, or 1.1%, in Wednesday's primary.
In a victory speech early on Thursday, she said she would approach the job of prime minister with "great reverence".
The senior Palestinian Authority negotiator, Saeb Erekat, said he hoped the result would lead to a return to stability.
The Islamist movement, Hamas, which controls the Gaza Strip, said it expected no change in Israel's policy towards the Palestinians.
'Extortion and demands'
Ms Livni is expected to meet later on Thursday with her three defeated rivals - Mr Mofaz, Interior Minister Meir Sheetrit and Public Security Minister Avi Dichter - in an attempt to form a united front before launching negotiations on forming a new coalition.
She also reportedly phoned the head of the Labour Party, Defence Minister Ehud Barak, to discuss continuing its participation in the governing alliance.
Correspondents say Labour's poor standing in the polls means it is likely to seek to maintain the coalition in order to avoid facing an early general election.
Earlier, Mr Sheetrit advised that Kadima "should form a coalition without giving in to Haredi [ultra-Orthodox Jewish] demands and extortion", thought to be a reference to the Shas party, a key member of the current government.
The chairman of Shas, Eli Yishai, was quick to lay out its conditions for taking part in a new coalition on Thursday, including ruling out any negotiations on Jerusalem's future and increasing child allowances.
"If Livni wants a government, she needs to comply with our demands," he said.
The centre-right opposition Likud party of former prime minister Binyamin Netanyahu, which is currently leading in the polls, immediately called for a general election.
"Forming a new government based on the votes of 431 Kadima members would be a legal farce," said Likud parliamentary whip Gideon Saar.
"The parties should display national responsibility, sit together and determine an agreed-upon date for new [parliamentary] elections," he added.
If she can form a fresh governing coalition within the next six weeks, Ms Livni will become Israel's first woman prime minister since Golda Meir stepped down in 1974.
The BBC's Tim Franks in Jerusalem says that will be no easy task, and if it were to end in failure, general elections will follow in a further three months.
'National responsibility'
According to the final results of Wednesday's Kadima leadership contest, Ms Livni won with 43.1%, or 16,936 votes. Mr Mofaz, a former defence minister and chief of staff of the Israeli military, came in a close second with 42%, or 16,505 votes.
The two other candidates, Mr Sheetrit and Mr Dichter, lagged far behind with 8.4% and 6.5% respectively.
In a victory speech early on Thursday morning, Ms Livni said that she would seek to form a new coalition government "as quickly as possible" and called for party unity.
"All the people who came to vote today expressed what they wish to happen in this country," she said.
"The national responsibility [bestowed] by the public brings me to approach this job with great reverence."
Ms Livni is seen as less hawkish than Mr Mofaz when it comes to the Palestinians and to dealing with Iran's nuclear ambitions.
Critics say Ms Livni, a former commercial lawyer and Mossad agent, also lacks political experience.
Israelis react to Tzipi Livni's win
Her supporters say she represents a break with the past.
Ms Livni is untainted by the kind of allegations of corruption and bribery that led to Mr Olmert's resignation and have damaged the reputation of Israeli politics.
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. An Israeli spokesman said the two would continue to meet until a new government was sworn in.
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