Mofaz’s supporters called for a recount, but Israeli media reported that he had called Livni to congratulate her on her victory and had rejected a legal adviser’s proposal that he appeal the results.

When the polls closed at 10.30 pm Wednesday, exit surveys indicated that Livni had swept to victory with a 10-point lead. But as counting of the nearly 40,000 votes progressed, the gap narrowed sharply. Before dawn, officials announced that Livni had won by 431 votes, according to Israel Radio.

Speaking outside her home in Tel Aviv, Reuters reported, Livni vowed to start work immediately on forming a new coalition that would let her succeed Olmert as prime minister.

The difference between Livni, a diplomatic 50-year-old lawyer who has led peace talks with the Palestinians, and Mofaz, a hawkish 59-year-old former general who has derided those talks, appears substantial.

If Livni fends off any possible legal challenge and succeeds in putting together a majority coalition of the 120-member Parliament, she will be the first woman to lead this country since Golda Meir in 1974. If not, the country will hold general elections three months later. Polls show the right-ring Likud party of Benjamin Netanyahu a very strong contender in such a race.

Olmert, the object of several investigations alleging that he took money illegally while mayor of Jerusalem and industry minister, called Livni to congratulate her and promise his full cooperation. He has agreed to step down once his replacement is chosen so that the police inquiry does not further interfere with matters of state, but he is likely to remain in a caretaker capacity until a government is formed. Coalition options are complex and the small victory clearly could be seen as a reduced mandate to form a government without general elections.

The current government, headed by the centrist Kadima party, includes the left-wing Labor party, the Pensioners party and Shas, an ultra-Orthodox Sephardic party. There have been sharp tensions between Livni and the Labor leader, Defence Minister Ehud Barak, but he seems likely to join her to seek to avoid elections that could carry Likud to power.

The Pensioners will pose no difficulties but Shas is more naturally inclined toward Likud, which advocates a tougher approach toward the Palestinians, the ending of peace talks with the Syrians and a solemn vow never to give up sovereignty over any part of Jerusalem to the Palestinians who seek its eastern part as their capital.

Shas, whose members have large families, also wants a big increase in child welfare allowances, which Livni says she opposes.

She could turn to Meretz, which is to the left of Labor. She has also said she would try to attract Likud. But Netanyahu, the Likud leader, said on Wednesday that joining Kadima in a government would be tantamount to joining the board of Lehman Brothers.