WASHINGTON (AP) — Republican senators on Tuesday welcomed a move by the director of national intelligence to snuff out leaks of classified information but insisted that a special counsel is needed to investigate the Obama administration and recent disclosures.

Four lawmakers, including Obama's 2008 GOP presidential rival John McCain, acknowledged that Americans were paying little attention to the issue, with immigration and health care drawing most of the focus. They held a news conference and released a letter to Attorney General Eric Holder renewing their weeks-old call for the appointment of an independent investigator. Republicans argue that the leaks were deliberate to enhance the president's record on national security as he seeks a second term.

"This administration cannot be trusted to investigate itself," Sen. John Cornyn, R-Texas, told reporters.

Holder has appointed two U.S. attorneys to lead a Justice Department inquiry into who leaked information about U.S. involvement in cyber-attacks on Iran and an al-Qaida plot to place an explosive device aboard a U.S.-bound flight. Holder has resisted calls for a special counsel, telling lawmakers recently that the two attorneys, Ron Machen and Rod Rosenstein, are experienced, independent and thorough.

To stem the leaks, Director of National Intelligence James R. Clapper announced two new steps on Monday. He said a question related to unauthorized disclosure of classified information would be added to the polygraph test used by intelligence agencies. He also said the inspector general for the intelligence community would lead any independent investigations that the Justice Department declines.

"That's to some degree closing the barn door," McCain said. "I think it's laudable that he has taken that step, but the fact is we have to find out how this happened and who did it."

The Republicans suggested that a congressional investigation may be warranted. Cornyn said he spoke to Sens, Joe Lieberman, I-Conn., and Susan Collins, R-Maine, the top members of the Senate Homeland Security and Governmental Affairs Committee, about a possible inquiry.

In the letter, at least 31 Republican senators say the leaks have risked national security as well as the lives of U.S. citizens and allies. They said that based on media reports, there could be many sources for the leaks within the administration.

The GOP lawmakers wrote that the inquiry by the two U.S. attorneys "does not ensure a full and thorough investigation free of influence. The U.S. attorneys are under your personal supervision. An outside special counsel, with the appropriate independence and authority, would ensure that the investigation remains untainted by even the appearance of politics or undue influence."

The investigation is just under way, but in an unusual step the lawmakers singled out by name national security adviser Thomas Donilon, citing various media reports. Asked about the mention of Donilon, McCain said, "I'm not ready to indict someone until the investigation is complete."

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  • Dianne Feinstein, Saxby Chambliss, Mike Rogers, C.A. "Dutch" Ruppersberger

    After a closed-door meeting with National Intelligence Director James Clapper, the four leaders of the House and Senate Intelligence Committees hold a news conference, on Capitol Hill in Washington, Thursday, June 7, 2012, to discuss the recent spate of classified national security information leaks. From left are Rep. C.A. "Dutch" Ruppersberger, D-Md., the ranking Democrat on the House Intelligence Committee; House Intelligence Committee Chairman Mike Rogers, R-Mich., Sen. Saxby Chambliss, R-Ga., vice-chair of the Senate Intelligence Committee, and Senate Intelligence Committee Chair Sen. Dianne Feinstein, D-Calif. (AP Photo/J. Scott Applewhite)

  • Dianne Feinstein, Saxby Chambliss, Mike Rogers, C.A. "Dutch" Ruppersberger

    After a closed-door meeting with National Intelligence Director James Clapper, the four leaders of the House and Senate Intelligence Committees hold a news conference, on Capitol Hill in Washington, Thursday, June 7, 2012, to discuss the recent spate of classified national security information leaks. From left Rep. C.A. "Dutch" Ruppersberger, D-Md., the ranking Democrat on the House Intelligence Committee; House Intelligence Committee Chairman Rep. Mike Rogers, R-Mich., Senate Intelligence Committee Chair Sen. Dianne Feinstein, D-Calif.; and Sen. Saxby Chambliss, R-Ga., vice-chair of the Senate Intelligence Committee. (AP Photo/J. Scott Applewhite)

  • Dianne Feinstein, Saxby Chambliss, Mike Rogers, C.A. "Dutch" Ruppersberger

    After a closed-door meeting with National Intelligence Director James Clapper, the four leaders of the House and Senate Intelligence Committees hold a news conference, on Capitol Hill in Washington, Thursday, June 7, 2012, to discuss the recent spate of classified national security information leaks. From left are, Rep. C.A. "Dutch" Ruppersberger, D-Md., the ranking Democrat on the House Intelligence Committee; House Intelligence Committee Chairman Rep. Mike Rogers, R-Mich., Senate Intelligence Committee Chair Sen. Dianne Feinstein, D-Calif.; and Sen. Saxby Chambliss, R-Ga., vice-chair of the Senate Intelligence Committee. (AP Photo/J. Scott Applewhite)

  • James Clapper

    Director of National Intelligence James Clapper, center, emerges from a closed-door meeting with the House and Senate Intelligence Committees aimed at stopping security leaks, Thursday, June 7, 2012, on Capitol Hill in Washington. (AP Photo/J. Scott Applewhite)

  • James Clapper

    Director of National Intelligence James Clapper, center, emerges from a closed-door meeting with the House and Senate Intelligence Committees aimed at stopping security leaks, Thursday, June 7, 2012, on Capitol Hill in Washington. (AP Photo/J. Scott Applewhite)

  • Jay Carney

    Press Secretary Jay Carney briefs reporters at the White House in Washington, Monday, June 4, 2012. (AP Photo/Charles Dharapak)

  • House Leader Boehner And Cantor Respond To Obama's Economic News Conference

    WASHINGTON, DC - JUNE 08: House Majority Leader Eric Cantor (R-VA) (L) and U.S. Speaker of the House John Boehner (R-OH) (R) respond to U.S. President Barack Obama's remarks on the U.S. economy June 8, 2012 in Washington, DC. During their remarks, Cantor said, 'Did he see the job numbers that came out last week? The private sector is not doing fine. And, frankly, I'd ask the president to stop engaging in the blame game.' (Photo by Win McNamee/Getty Images)

  • House Leader Boehner And Cantor Respond To Obama's Economic News Conference

    WASHINGTON, DC - JUNE 08: House Majority Leader Eric Cantor (R-VA) (L) and U.S. Speaker of the House John Boehner (R-OH) (R) respond to U.S. President Barack Obama's remarks on the U.S. economy June 8, 2012 in Washington, DC. During their remarks, Cantor said, 'Did he see the job numbers that came out last week? The private sector is not doing fine. And, frankly, I'd ask the president to stop engaging in the blame game.' (Photo by Win McNamee/Getty Images)

  • House Leader Boehner And Cantor Respond To Obama's Economic News Conference

    WASHINGTON, DC - JUNE 08: U.S. Speaker of the House John Boehner (R-OH) arrives to respond to U.S. President Barack Obama's remarks on the U.S. economy June 8, 2012 in Washington, DC. During remarks with House Majority Leader Eric Cantor, Cantor said, 'Did he see the job numbers that came out last week? The private sector is not doing fine. And, frankly, I'd ask the president to stop engaging in the blame game.' (Photo by Win McNamee/Getty Images)

  • House Leader Boehner And Cantor Respond To Obama's Economic News Conference

    WASHINGTON, DC - JUNE 08: House Majority Leader Eric Cantor (R-VA) (L) and U.S. Speaker of the House John Boehner (R-OH) (R) respond to U.S. President Barack Obama's remarks on the U.S. economy June 8, 2012 in Washington, DC. During their remarks, Cantor said, 'Did he see the job numbers that came out last week? The private sector is not doing fine. And, frankly, I'd ask the president to stop engaging in the blame game.' (Photo by Win McNamee/Getty Images)

  • House Leader Boehner And Cantor Respond To Obama's Economic News Conference

    WASHINGTON, DC - JUNE 08: U.S. Speaker of the House John Boehner (R-OH) (R) and House Majoirty Leader Eric Cantor (R-VA) (L) respond to U.S. President Barack Obama's remarks on the U.S. economy June 8, 2012 in Washington, DC. During Cantor's remarks, Cantor said, 'Did he see the job numbers that came out last week? The private sector is not doing fine. And, frankly, I'd ask the president to stop engaging in the blame game.' (Photo by Win McNamee/Getty Images)