(Adds background, Wolfowitz memo to World Bank staff)

WASHINGTON, April 17 (Reuters) - The U.S. Defense Department ordered a contractor to hire a World Bank employee and girlfriend of then-Pentagon No. 2 Paul Wolfowitz in 2003 for work related to Iraq, the contractor said on Tuesday.

A spokeswoman for Science Applications International Corp., or SAIC, said the Defense Department's policy office directed the company to enter a subcontract with Shaha Riza, under which she spent a month studying ways to form a government in Iraq.

Wolfowitz, an Iraq war architect who left the Pentagon in 2005 to become president of the World Bank, is under fire for overseeing a high-paying promotion for Riza after he took the helm of the poverty-fighting global lender.

He has made fighting corruption in the developing world a hallmark of his tenure.

A Pentagon spokesman said he had no information about the contract with Riza or SAIC's statement.

Melissa Koskovich, a spokeswoman for SAIC, said the contractor "had no role in the selection of the personnel who comprised the Iraq Governance Group under this contract."

SAIC said Riza's contract lasted from April 25 to May 31, 2003. She was paid expenses but no salary during her trip to Iraq, at her request, according to the contractor.

The World Bank's board is examining Wolfowitz's role in helping to arrange Riza's promotion and the bank's staff association has called for his resignation.

The controversy hung over the spring meetings of the International Monetary Fund and World Bank this past weekend, which brought together top finance and development officials from around the globe.

In a striking rebuke, the bank's member governments said on Sunday they were troubled by the matter and that it was crucial the bank's credibility not be tarnished.

Wolfowitz said he intended to stay in his job.

In an e-mail to bank staff on Tuesday, he sought to ease concerns the episode might derail bank business.

"I want to reassure you that we conducted a full agenda of bank business with the governors, heads of delegation and various groups who attend the spring meetings," he said, referring to the weekend gathering.

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