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In his opening statement, Committee Chairman Harry Waxman, a Californian Democrat, said he prefers to issue subpoenas as a "last resort," adding that he felt he had "hit a brick wall" with Rice.
"For four years, I have been trying to get information from Rice on a variety of issues, including the reference to uranium and Niger in the president's 2003 State of the Union speech," Waxman said.
"My request is simple: I would like Secretary Rice to suggest a date that would be convenient for her to testify before our committee," he said.
House Minority Leader John Boehner, a Republican from Ohio, quickly denounced the committee's actions, saying it is merely a "partisan show."
The committee also passed issuing subpoenas to Republican National Committee (RNC) chairman Mike Duncan and for the e-mails White House officials composed on RNC e-mail accounts with regard to the firing of eight U.S. Attorneys.
The committee's move is part of the Democratic-led Congress's ongoing investigations of the conducts of the Bush administration.