By Jeffrey Heller JERUSALEM, May 29 (Reuters) - Former Prime Minister Ehud Barak won on Tuesday the first round of the Israeli Labour Party's leadership election and will face an ex-security chief in a runoff vote next month, official results showed. Although Barak and former secret service chief Ami Ayalon have called on Prime Minister Ehud Olmert to quit over his handling of last year's Lebanon war, both have stopped short of saying they would pull Labour out of his governing coalition. Official results with all but one polling station counted showed Barak with 36 percent of the vote to Ayalon's 31 percent, figures short of the 40 percent needed to avoid a June 12 runoff. The outcome of the first round of voting among some 104,000 Labour members effectively toppled Defence Minister Amir Peretz as the centre-left party's chairman. His unpopularity, along with Olmert's plunged in the wake of the costly conflict last July and August with Lebanon's Hezbollah guerrillas. An official inquiry found that both had mishandled the war, stirring public pressure for them to resign. Barak, a former general and Israel's most decorated soldier, served as prime minister from 1999 to 2001. During his term, he held unsuccessful peace talks with Syria and the Palestinians. He was defeated by right-winger Ariel Sharon in a 2001 national election after a Palestinian uprising erupted. The first-round Labour triumph -- no one candidate had been expected to pass the 40 percent mark -- was a key step towards a political comeback for Barak, who turned to international business consultancy after his 2001 defeat. But several polls have suggested that Ayalon, who also has a military pedigree as a former admiral, will emerge on top in the runoff. Both men have said they want to secure Israel's future by making peace with its Arab neighbours and have agreed to keep Labour as the ranking junior partner in Olmert's government for now. Olmert's political future, however, is unclear. The Winograd Commission investigating the Lebanon war issues a final report in August. Further criticism of Olmert by the government-appointed panel could bring heavier public pressure on the veteran politician to step down. Peretz has already said he will quit as defence minister regardless of the result of the Labour vote. The new chairman is likely to take the post, which is reserved for Labour under its coalition agreement with Olmert's centrist Kadima party. The first round voting took place amid rocket attacks by Palestinian militants in Gaza. One such strike killed an Israeli on Sunday in Peretz's hometown of Sderot. Israel has countered with air raids against Gaza gunmen.
