JERUSALEM, July 30 (Reuters) - Israeli Prime Minister Ehud Olmert said on Wednesday he would step down after his ruling Kadima party chooses a new leader in a Sept. 17 internal election in which he will not run.

"I have decided I won't run in the Kadima movement primaries, nor do I intend to intervene in the elections," Olmert said in a surprise announcement from his official residence in Jerusalem.

"When a new (Kadima party) chairman is chosen, I will resign as prime minister to permit them to put together a new government swiftly and effectively."

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