WASHINGTON (CNN) -- Karl Rove, President Bush's longtime political guru, refused to obey an order to testify before a House Judiciary Committee hearing Thursday.

Karl Rove's lawyers says he is immune from a congressional subpoena.

Rove's lawyer asserted that Rove was "immune" from the subpoena the committee had issued, arguing that the committee could not compel him to testify due to "executive privilege."

The panel is investigating allegations that Rove and his White House allies dismissed U.S. attorneys and prosecuted officials who they saw as political opponents.

The panel subpoenaed Rove in May after his lawyer, Robert D. Luskin, made clear the former White House deputy chief of staff would not appear voluntarily.

Luskin responded immediately that Rove still would not appear, prompting a threat of prosecution from the Judiciary Committee chairman, Rep. John Conyers, a Michigan Democrat, and Rep. Linda Sanchez, a California Democrat who chairs the subcommittee on commercial and administrative law.

"A refusal to appear in violation of the subpoena could subject Mr. Rove to contempt proceedings, including statutory contempt under federal law and proceedings under the inherent contempt authority of the House of Representatives," Conyers and Sanchez wrote.

"We are unaware of any proper legal basis for Mr. Rove's refusal to even appear today as required by the subpoena," Sanchez said Thursday morning when Rove failed to show up. "The courts have made clear that no one -- not even the president -- is immune from compulsory process. That is what the Supreme Court rules in U.S. v. Nixon and Clinton v. Jones."

In May, Conyers contrasted Rove's refusal to testify before Congress with his paid work as a commentator for the Fox News Channel and Newsweek magazine.

"Although he does not seem the least bit hesitant to discuss these very issues weekly on cable television and in the print news media, Mr. Rove and his attorney have apparently concluded that a public hearing room would not be appropriate. Unfortunately, I have no choice today but to compel his testimony on these very important matters."

Rove's lawyer cited a letter from the Justice Department saying Rove is "constitutionally immune from compelled congressional testimony." He said Rove is willing to submit to an "informal interview" or to answer written questions about the prosecution of former Alabama Gov. Don Siegelman, whose ouster Rove is accused of orchestrating.

"Threatening Mr. Rove with sanctions will not in any way expedite the resolution of the issue," Luskin wrote in a letter to the panel on Wednesday.

Luskin noted in May that his client had already received a separate subpoena from the Senate Judiciary Committee. "While the [House] committee has the authority to issue a subpoena, it is hard to see what this will accomplish, apart from a 'Groundhog Day' replay of the same issues that are already the subject of litigation," the lawyer wrote, referring to a movie in which a person lives the same day over and over again.

Luskin added that "issues of executive privilege and separation of powers" could limit Rove's testimony.

In response, Conyers said the two committees are focusing on different matters, with the House committee delving into the prosecution of the former Alabama governor, a Democrat who lost his bid for re-election in 2002 and was convicted on corruption charges in 2006.

Conyers also noted that other former White House officials have testified under subpoena in the past and have dealt with issues of executive privilege on a case-by-case basis. "Mr. Rove should follow the same course," he said.

Rep. Lamar Smith of Texas, the top Republican on the House Judiciary Committee, called the subpoena "a sham."

The Democratic-controlled Congress has been battling for months to force the White House to disclose information about the firing of the attorneys and the prosecution of Siegelman.

Current and former White House aides have refused to testify, citing executive privilege.

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