Attorney General Eric H. Holder Jr.’s direct involvement in the Justice Department’s decisions to spy on the press should disqualify him from heading any review of the unfolding controversy, Republicans said Sunday.

Questions have been raised about the attorney general’s role in two Justice Department investigations of leaks, one involving a massive seizure of Associated Press phone records and another an aggressive probe of Fox News reporter James Rosen’s private emails.

According to multiple media reports, Mr. Holder personally approved targeting Mr. Rosen. He earlier told Congress that he had recused himself from the decision to seize AP phone records.

President Obama, responding to critics from both parties who say the Justice Department is undermining press freedoms, said Thursday he has directed Mr. Holder to lead a “review.” That idea has been flatly rejected by Republicans, several of whom voiced their objections on Sunday’s political talk shows.

“A total conflict of interest,” Sen. Tom Coburn, Oklahoma Republican, said Sunday on CBS’ “Face the Nation.”

“You cannot investigate yourself. Allowing the very person that authorized the two things we are aware of today to investigate whether he did that appropriately is inappropriate,” Mr. Coburn said. “There’s an inherent conflict of interest in me judging whether I did something and reporting it to the president.”

Mr. Coburn stopped short of calling for a special prosecutor, but Sen. Lindsey Graham, South Carolina Republican, appeared on “Fox News Sunday” and said it was “time to have a special counsel to come forward or some independent group to look at it.”

Senate Majority Whip Richard J. Durbin, Illinois Democrat, wouldn’t go that far, but he acknowledged he has questions about Mr. Holder’s role.

“I heard Sen. Graham call for special counsel. I’m not ready to do this at this point. I’d like to know if Holder has any conflict in here beyond what we’ve heard when it comes to the Fox case,” Mr. Durbin said on the Fox program.

Another Democrat, Sen. Charles E. Schumer of New York said “the system is clearly broken” and that he and Mr. Graham will reoffer their proposal, with the bipartisan support of six other senators, for a “media shield law” that would tighten judicial oversight of Justice Department and law enforcement.

“We’ll be announcing that we have four Democrats and four Republicans another ‘Gang of Eight,’” Mr. Schumer said on CBS’ “Face The Nation.” He did not specify who would join him and Mr. Graham.

The proposal would require the government to first go before a judge to ask a news organization to divulge sources. That judge would “impose a balancing test” between free press and government need for the information.

“You always need set rules and an independent arbiter. We have neither now,” he said.

The Department of Justice has come under fire amid revelations that Mr. Holder personally approved an investigation of Mr. Rosen after his 2009 Fox News story on North Korean missile tests that cited intelligence community sources.

In an effort to uncover what some administration officials considered a national security leak, Mr. Rosen was named a potential criminal “co-conspirator” and Mr. Holder signed off on warrants to allow agents to track the reporter’s movements at the State Department and monitor his phone records and emails.

“James Rosen is a lot of things, but a criminal co-conspirator he is not,” Mr. Graham said. “We’re beginning to criminalize journalism, and I think that should worry us all.”

Mr. Graham also called for a special counsel to investigate the IRS targeting of conservative groups seeking tax-exempt status.

The president said Thursday that he was “troubled by the possibility that leak investigations may chill the investigative journalism that holds government accountable.”

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