WASHINGTON, March 13 (Reuters) - U.S. Defense Secretary Robert Gates is unlikely to choose a new commander for the Iraq and Afghanistan wars before May, his spokesman said on Thursday.

Adm. William Fallon, head of the U.S. Central Command headquarters responsible for the Middle East, announced on Tuesday he would quit after a magazine reported he was pushing President George W. Bush to avoid war with Iran.

Pentagon press secretary Geoff Morrell said Gates did not pressure Fallon to resign and did not know the resignation was coming, so the department was not ready to name a successor.

"We are only beginning to turn our focus ahead to looking at potential candidates for a replacement," he said.

"I do not believe we will have this until the month of May, until at least the month of May," Morrell said.

Morrell first said Gates would not recommend a new Central Command chief to Bush before Gen. David Petraeus, the top commander in Iraq, testifies on Capitol Hill about the war in April.

Asked if that was because Gates wanted to speak to Petraeus as a candidate for the job, Morrell said no and extended the likely time frame for officials to reach a decision to May.

"I think they want to conduct an exhaustive search and look for the best possible candidates and then make a decision on a recommendation for the president," he said.

Gates said on Tuesday that Army Lt. Gen Martin Dempsey, Fallon's deputy, would take temporary charge of Central Command when the admiral retires at the end of this month. (Reporting by Kristin Roberts, Editing by David Wiessler)

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