The race between current Kadima Party chief Tzipi Livni and Shaul Mofaz is expected to be closely fought. Whoever wins will try to wrest power from Prime Minister Benjamin Netanyahu when Israelis next go to national elections, currently scheduled for October 2013 AP reported.
Livni, 53, served as foreign minister in the previous government, and was lead negotiator with the Palestinians in the last extended round of peace talks that began in Annapolis, Maryland, in late 2007 but never seriously recovered after Israel's offensive in the Gaza Strip a year later.
"I am very calm about the results," Livni told Ynet, the website of the Yediot Ahronot newspaper.
Mofaz, 63, was chief of the Israeli military and later defense minister during the four-year Palestinian uprising that broke out in late 2000. Although he favors peacemaking with the Palestinians, he oversaw a harsh response against Palestinian militant groups, including the assassination of militant leaders, that stirred controversy abroad.
"I intend to win the general elections and to replace Netanyahu," Ynet quoted Mofaz him as saying.
The two also ran against each other in Kadima's last leadership contest in September 2008, which Livni won by a slim margin of several hundred votes.
Kadima was founded in November 2005 by then-Prime Minister Ariel Sharon, who defected from the Likud Party with many of its top officials to break free of opposition within Likud to some of his peace moves. Sharon had a calamitous stroke soon after, but despite his incapacitation, he remained the inspiration that propelled Kadima to power in early 2006 elections.
With Ehud Olmert at the helm, Kadima governed from 2006 to 2009. A cascade of corruption allegations forced him to step down, and the party's fortunes have waned since February 2009 national elections that brought Likud leader Benjamin Netanyahu to power.
In the 2009 vote, Kadima won the most parliament seats, 28 of 120, and had a chance to form Israel's government. But Livni couldn't marshal enough allies to put together a governing coalition and Netanyahu, head of the Likud, was given the task.
Kadima was sidelined to the opposition. Internally, too, it has suffered, with polls showing some former backers defecting to the Labor Party and others expected to line up behind a former television personality, Yair Lapid, who has announced plans to set up his own party.
Recent polls show Kadima would win just a dozen seats if national elections were to be held today, while Netanyahu and his hawkish allies would be well-placed to lead the government again.
Voting in the Kadima race opens at 10 a.m. (0800 GMT) Tuesday and closes 12 hours later. Some 95,000 Kadima members are eligible to vote. Official results are expected after midnight, but indications of a winner could come earlier, based on voter turnout.