The leading candidates for the leadership of Israel’s second largest party appear to be heading to a runoff vote in two weeks that may determine not only who will lead the party but also the longevity of the current government.

The top candidates in the highly anticipated Labor primary vote, held last night, are a former prime minister, Ehud Barak, 65, who is attempting to return to the prime minister’s office, and a more dovish former general, Ami Ayalon, 61, who is considered a fresh new face in top-tier Israeli politics.

To remain in power, Prime Minister Olmert must have the support, in the 120-member Knesset, of the Labor Party. If Labor bolts, the country will hold new general elections. Currently, however, national polls project that both Labor and Mr. Olmert’s party, Kadima, would lose votes in a general election, while the much smaller Likud Party, headed by Benjamin Netanyahu, stands to gain significantly.

Mr. Barak, who needs to overcome the public’s resentment over his failure in 2001 to deliver peace or security, is seeking to rebuild his security credentials by becoming Mr. Olmert’s defense minister. Mr. Ayalon, whose campaign was based largely on his freshness as candidate, may be more amenable to leaving the government earlier, according to political analysts.

Projections broadcast by two of Israel’s leading television stations after the primary vote ended last night showed contradictory results. Channel 1 projected that Mr. Barak would win with 38% of the vote, leaving Mr. Ayalon with 36%. According to Channel 2, Mr. Ayalon was leading, with 39%, over Mr. Barak, with 33%. If no candidate garners 40% of the vote, a runoff between the top two candidates will determine the leadership of the party.

The current Labor leader, Defense Minister Amir Peretz, was projected last night to receive as little as 20% of the vote. Two other candidates, Ophir Paz-Pines and Danny Yatom, appeared to be headed toward the single digits.

Mr. Peretz came under heavy criticism in an interim report from a government-appointed panel known as the Winograd Commission, which investigated last year’s war against Hezbollah. Seen as miscast at the top of Israel’s defense establishment, Mr. Peretz said he would leave his post to become finance minister, promoting a populist, “social”-oriented economy.

In contrast to Mr. Peretz, Mr. Barak has said he would keep the Labor-Kadima coalition intact only if Mr. Olmert immediately announces a date for a new national election. Mr. Ayalon has said he would remain in a coalition with Kadima — which translates as “Forward” in Hebrew —only if Mr. Olmert resigns as prime minister.

Many Israeli political analysts say the next national election will pit Labor, under a new leadership, against the Likud Party. Mr. Netanyahu is leading in national polls against both of the Labor candidates. But those polls could change as the Labor Party restructures.

“Assuming that Kadima continues to go backward, Labor could give a good run for Likud’s money, boosted with an even team based on defense and dovish credentials, as well as a mildly social-based economy,” a columnist for the Israeli daily Ma’ariv, Ben Caspit, wrote.

Mr. Barak, a former army chief of staff and prime minister between 1999 and 2001, ran his Labor campaign on his defense expertise. “Who would you trust to lead in a time of war?” he said as late as yesterday. He also said that only under his leadership could Labor beat Mr. Netanyahu in an upcoming election.

Mr. Ayalon, 61, a former navy commander who ended his military career as chief of the Israeli internal intelligence service, Shabak, has emerged in recent years as a leader of Israel’s doves. In 2003, Mr. Ayalon and a Palestinian Arab activist, Sari Nusseibeh, launched a blueprint for a peace agreement that they hoped would garner popular support.

The biggest hurdle for Mr. Ayalon, who is largely unknown outside Israel, appeared to be his leadership inexperience, which was also one of the most attractive features of his campaign. While Mr. Ayalon has admitted to making mistakes, his supporters have reminded voters that when Mr. Barak left politics, he was largely seen as aloof and unable to create internal and external alliances.

“What is more difficult to make up for, a lack of character or a lack of experience?” a political columnist for the Israeli daily Ha’aretz and a supporter of Mr. Ayalon’s, Akiva Eldar, said.