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“Until now, everyone believed that the decisions regarding Fast and Furious were confined to the Department of Justice,” said Brendan Buck, a spokesman for House Speaker John A. Boehner, Ohio Republican.

“The White House decision to invoke executive privilege implies that White House officials were either involved in the Fast and Furious operation or the cover-up that followed. The administration has always insisted that wasn’t the case. Were they lying, or are they now bending the law to hide the truth?” Mr. Buck said.

It’s also an uncomfortable position for a president who hails his administration’s transparency, for example, in matters such as releasing White House visitor logs. As a candidate, Mr. Obama pledged to enforce “a new standard of openness.”

“We’re constantly trying to open up the process,” Mr. Obama said in January 2010.

When he was campaigning for the presidency in 2007, Mr. Obama promised to reserve the use of executive privilege for cases of national security or “traditionally sensitive matters.”

In 2004, Mr. Fisher noted, the Bush administration initially refused to allow National Security Adviser Condoleezza Rice to testify in public before the 9/11 commission. White House Counsel Alberto Gonzales argued that the separation of powers was at stake, but he reversed himself and allowed Ms. Rice to testify.

During Mr. Bush’s presidency, the Republican tried to greatly expand presidential powers, both to prevent disclosure of internal White House communications and to disregard portions of laws with which he didn’t agree.

Mr. Clinton claimed executive privilege to try to shield his wife, first lady Hillary Rodham Clinton, from questions about the Whitewater real estate scandal and the Monica Lewinsky affair. Courts rejected his claims in both cases.

A report in 2008 by the Congressional Research Service said the administrations of Presidents George H.W. Bush and Mr. Clinton took the position that executive privilege extended to recommendations made to senior officials and communications of senior policymakers throughout the executive branch, including within the White House or between the White House and any federal department or agency.

Researcher John Sopko contributed to this report.