JERUSALEM — Israel’s popular foreign minister faced off against a former military chief today in the leadership race for the ruling Kadima party — an election that could determine the country’s next prime minister.

In a last-minute decision, the party extended voting for an extra hour because of overcrowding at the polling stations, a Kadima Party member, Otniel Schneller, who is identified with Foreign Minister Tzipi Livni, said

Ms. Livni, who hopes to become Israel’s first female prime minister in more than three decades, held a strong lead over a former chief of staff and defense minister, Shaul Mofaz, in opinion polls ahead of the vote. But Mr. Mofaz insisted the polls were inaccurate and predicted victory for himself.

It remained unclear whether either candidate would break the 40% threshold needed to avoid a runoff. Two other candidates, a Cabinet minister, Meir Sheetrit, and a former director of the Shin Bet security service, Avi Dichter, lagged far behind in the polls.

Israeli media reported that four hours before the new closing time of 11 p.m., only 30% of the eligible Kadima voters had cast their ballots. In Israeli elections, voting usually picks up in the evening after working hours.

Analysts say Ms. Livni’s chances depend on a high turnout. Israeli media reported the request to extend the voting came from the Livni camp, but Mr. Schneller would not confirm that.

Kadima convened the primary to choose a successor to Prime Minister Olmert, who is being forced from office by a corruption scandal. Whoever wins has a good chance of becoming the next prime minister.

Ms. Livni, a former lawyer and one-time agent in the Mossad spy agency, is a soft-spoken diplomat who has played a central role in peace talks with the Palestinian Arabs and prefers negotiation to confrontation.

“You can determine today what the character of Kadima will be,” Ms. Livni, casting her vote in Tel Aviv, said. “You can determine today if you really have had enough of old-time politics. Come and vote, bring your children, and show them how you are changing the country.”

Mr. Mofaz takes a tougher line, demanding the Palestinian Arabs fulfill a series of conditions before a final deal can be hammered out. He also is more willing to order military action in times of crisis. He spooked global oil markets last June when he said Israel would have “no choice” but to attack Iran if sanctions fail to curb its nuclear program. He has since backed away from those comments.

Mr. Mofaz insists that he is the best person to run this security-sensitive country as it pursues peace with the Palestinian Arabs and Syria, and eyes what it says is Iran’s covert nuclear weapons program. He has boldly predicted he will take exactly 43.7% of today’s vote.

“The state of Israel stands before major challenges in the coming years and needs a strong leader who has the courage to decide and the ability to act,” he told Army Radio.

Whoever wins could soon make history. Ms. Livni hopes to become Israel’s first female prime minister since Golda Meir resigned in 1974.

Male rivals have called Ms. Livni “weak” and “that woman.” And there is talk about ultra-Orthodox Jewish lawmakers being uncomfortable with the idea of a female leader.

Ms. Livni has played down the gender issue. “The fact that I’m a woman doesn’t make me a weak leader,” she told the Jerusalem Post last week. “I have no problem pulling the trigger when necessary.”

Mr. Mofaz, meanwhile, hopes to become the first Israeli of Sephardic, or Middle Eastern, descent to lead the country. Sephardic Jews have long complained of discrimination at the hands of Ashkenazi, or European Jews. Mr. Mofaz was born in Iran and immigrated to Israel as a child.

About 74,000 registered party members were eligible to vote in today’s election. A candidate must receive at least 40% of the votes in order to win outright. Otherwise, a runoff will be held between the top two vote-getters next week.

A Kadima supporter in Tel Aviv, Joyce Amiel, said she was voting for Ms. Livni “mainly because she is a woman, even though her positions are not clear. We think she would do the best job. We want her to win.”

In the central city of Kfar Saba, voter Beni Shmeterling said he was voting for Mr. Mofaz. “The state of Israel needs someone who is experienced in security issues,” he said. “This is not a reality show. We need someone serious.”

The primary is Kadima’s first since it was founded by then-Prime Minister Ariel Sharon in 2005. Mr. Sharon suffered a debilitating stroke in early 2006, and Mr. Olmert subsequently led the party to victory in elections.

Mr. Olmert, who is under police investigation over his finances, has said he will resign as soon as Kadima has a new leader. But whoever wins the primary does not automatically become prime minister.

Kadima is the largest party in a four-member governing coalition, and the new leader will have just over a month to put together a new alliance. If that fails, the country will go to elections in early 2009, a year and a half ahead of schedule. Olmert will remain as a caretaker leader until a new coalition emerges.