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By Dan Williams

WASHINGTON, Aug 1 (Reuters) - Israel's peace efforts with Syria should continue, without preconditions, after Prime Minister Ehud Olmert steps down, a candidate to succeed him said on Friday.

"My opinion and my goal will be to continue to speak to the Syrians without preconditions," Deputy Israeli Prime Minister Shaul Mofaz said in a speech. "The way is - peace for peace."

Olmert and Syrian President Bashar al-Assad announced in May they we holding Turkish-mediated negotiations. But Olmert, dogged by corruption scandals, said earlier this week he would resign after his party picks a new leader in September.

Public statements suggested the sides remain divided on core issues like Israel's occupation of the Golan Heights and Syria's ties to Iran, Lebanese Hezbollah and Palestinian Hamas.

Syria has demanded the return of the Golan Heights before serious talks can take place. Mofaz, a former defense minister, has come out against any plan by Olmert to return the Golan. Olmert says he had made no such undertaking to the Syrians.

Foreign Minister Tzipi Livni has the edge in the ruling Kadima party race to replace Olmert, but Mofaz is her closest rival within the party, and contenders in other parties are vying for the job as well.

Though Mofaz, as chief of Israel's armed forces, led crackdowns on a Palestinian revolt that erupted in 2000, on Wednesday he cast himself as a potential peacemaker.

"As a father who has three children in the military, I want peace for them," he said.

"I will do my best to achieve peace with our neighbors ... Our first priority should be the Palestinians but there are some problems, some obstacles," he said, alluding mainly to the 2007 takeover of Gaza by Hamas. (Editing by Anthony Boadle)

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