JERUSALEM — Tzipi Livni, who not long ago was a popular and leading force in Israeli politics, lost the leadership of her centrist Kadima Party on Tuesday by a large margin to an archrival, according to results of the primary election.

The victory of Shaul Mofaz, a former military chief and defense minister and Kadima’s longstanding No. 2, left Ms. Livni’s political future in question. It also raised the prospect of a broader political shift, with analysts and commentators predicting that Mr. Mofaz would be more inclined than Ms. Livni to join a governing coalition led by Prime Minister Benjamin Netanyahu, and his right- leaning Likud Party.

Mr. Mofaz is inheriting a party less than a decade old and much weakened from the days when it was the governing party, from 2006 to 2009. Kadima’s period in opposition since has been lackluster under Ms. Livni. It remains the largest party in Parliament, but recent polls indicate that it has lost about half its support, making it just another contender in the crowded field of Israeli politics.

With attention in Israel and Washington focused on how to deal with Iran’s nuclear ambitions, Ms. Livni’s flagship policy for Kadima — a negotiated peace with the Palestinians on the basis of a two-state solution — has seemed increasingly irrelevant.

Mr. Netanyahu’s government has bent more leftward than many Israelis had expected, endorsing the two-state solution in principle and agreeing to a 10-month freeze in settlement construction, said Abraham Diskin, a political scientist at the Hebrew University of Jerusalem. The freeze expired in September 2010, and the Palestinians have refused to return to negotiations without a new settlement moratorium.

“The majority of Israelis believe that the Palestinians are responsible for the lack of progress,” Professor Diskin said, adding, “That only increases the popularity of the government and decreases that of Kadima.”

Mr. Mofaz has promoted his own plan for a provisional Palestinian state in 60 to 65 percent of the West Bank, in addition to Gaza, without initially removing any Israeli settlements.

Both Mr. Mofaz, 63, and Ms. Livni, 53, were once Likud ministers. Ms. Livni joined Kadima at its founding in November 2005 by Israel’s longtime leader, Ariel Sharon, shortly before the major stroke that has left him in a coma. Mr. Mofaz joined a few weeks later.

Analysts have increasingly questioned the cohesiveness of the party, which draws from both left and right. Some have even speculated that after the primary, Kadima might break up.

Mr. Mofaz, who was born in Iran and immigrated to Israel with his family at the age of 9, won about 61.7 percent of the vote to Ms. Livni’s 37.2 percent. About 45 percent of Kadima’s 95,000 members cast ballots.

Ms. Livni said she had called Mr. Mofaz to congratulate him, but would not say whether she intended to remain in Kadima.

Both candidates wrote articles appealing to voters that ran side by side on Tuesday in the newspaper Yediot Aharonot.

Mr. Mofaz pledged that a Kadima Party under his leadership would focus on social justice issues in Israel. “Starting from tomorrow, Israel will have a fighting and relevant opposition,” he wrote.

Ms. Livni echoed the belief of some political analysts here that Mr. Mofaz would be more likely to join a Netanyahu-led government, saying that he would turn Kadima into “Likud B,” an accusation Mr. Mofaz strenuously denied in an interview with Israel Radio as voting was under way on Tuesday.

Critics inside and outside Kadima have faulted Ms. Livni for what they say is her ineffectiveness as an opposition leader. She was unable to form a governing coalition in 2008 after her predecessor as Kadima’s leader, Ehud Olmert, resigned as prime minister amid a deepening corruption investigation, a failure that led to early elections.

In the 2009 elections, the party won 28 seats to Likud’s 27. But Ms. Livni again was unable to put together a coalition, then refused to join Mr. Netanyahu’s government, a decision many critics viewed as a mistake.

“I stood by the principles that are important to you,” she wrote in Yediot Aharonot. “For those principles, I went into opposition instead of taking a job in the Netanyahu government.”

Ms. Livni has also been criticized for her political absence during the huge social justice protests last summer when hundreds of thousands of Israelis demonstrated for affordable housing and against the high cost of living.

Mr. Mofaz has presented himself as more attuned to social issues, but the center-left Labor Party under its recently elected leader, Shelly Yacimovich, is far more identified with the social struggle in Israel.

The political center also has a new contender, Yair Lapid, a popular television host whose father was a well-known politician and journalist. Mr. Lapid announced in January that he was entering politics. Although he has not yet formed a party, polls have indicated that it would drain votes away from Kadima. (Copyright 2012 The New York Times Company 03/28/12)