Jerusalem — Tzipi Livni has begun the delicate task of assembling a ruling coalition in Israel after winning the leadership of the Kadima Party by a wafer-thin margin.

Three exit polls had suggested a 10% winning margin in the vote on Wednesday, but in the end Ms. Livni, the foreign minister, defeated Shaul Mofaz, the transport minister and her closest rival, by only 431 votes. After results were announced, Ms. Livni said: “The national responsibility [bestowed] by the public makes me approach this job with great awe.”

She made a rallying call for party unity and urged supporters of Mr. Mofaz and the two other losing candidates to put aside their differences.

“The rivalry is over,” she said. “We have common goals. We are beginning to make a change and the national task is quickly to establish stability. There are opportunities that need to be promoted and there is economic instability.” Mr. Mofaz said before the vote that if he lost he would give his full support to Ms. Livni.

Her attempts to become prime minister at the head of a working coalition received a major boost when Eli Yishai, the leader of the orthodox Shas movement, indicated that he would be willing to serve in a cabinet under her leadership.

There had been doubts over whether Shas would support a government led by Ms. Livni, who has served as Israel’s lead negotiator in peace talks with the Palestinians Arabs. She favors shared access to Jerusalem’s holy sites.

Shas is bitterly opposed to any division of Jerusalem.

Before a meeting last night, Mr. Yishai said he preferred to focus on a more mundane issue — whether Ms. Livni would promise to honor welfare payments — not the future of Jerusalem.

“She must provide answers to poverty. We won’t give up on our ideals, whether you call them [child] allowances, assistance, subsidies or grants to families with children,” he said.