Faulk described the al-Yawer calls as "courting, wooing and pillow talk" with an Iraqi woman he would later marry Nasrin Barwari, the minister of public works in the interim government.
Al-Yawer was the first President of Iraq's interim government between 2004 and 2005.
At the same time, U.S. intelligence was monitoring his private calls, al-Yawer was flown to Washington to meet President George Bush in the White House.
"I'm really honored you're here," said President Bush as he greeted al-Yawer in front of reporters in the Oval Office.
Al-Yawer, now divorced, could not be reached for comment. His ex-wife told ABC News she did not want to comment on the allegation that her private phone calls with her then fiancé were being intercepted by U.S. intelligence.
The NSA declined to comment on the specifics of Faulk's allegations involving al-Yawer and Blair.
In a statement, a spokesman said the agency follows all laws.
The Inspector General for the NSA is reported to be conducting an investigation into the allegations by Faulk and another former military intercept operator, Adrienne Kinne, about listening to calls between American citizens.
The Senate Intelligence and Judiciary Committees also are investigating the allegations about calls involving American citizens.
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