Sen. John Cornyn (R-Texas) today challenged Deputy Attorney General James Cole on recent — and potentially coordinated — national security leaks, further pressuring the administration to respond to GOP charges that White House officials might have violated the law by leaking classified information.

Cole, appearing before the Senate Judiciary Committee on a separate topic, said that it would be a crime for a government employee to divulge classified information to the media. However, he also said a series of articles in the New York Times that appear to include classified material do not merit a special prosecutor.

“It troubles me that anybody who has classified information, and lawfully has it, would then disclose it in violation of their duties to keep that classified information secret,” Cole said.

Cornyn asked Cole whether “it is a crime to leak classified information on the part of a government employee.”

“Without going into all the details, generally, yes, it is, Senator,” Cole said.

Lawmakers have cited several high-profile stories in national media outlets as the basis for their challenge to the administration. Chief among the pieces in question are a lengthy New York Times story on a terrorist “kill list,” another New York Times piece this week about Obama’s decision to begin cyberattacks on Iranian nuclear enrichment sites and yet another that reported extensively on the White House’s drone policies.

Cole declined to say whether the Justice Department would pursue an investigation of the leaks because of the classified nature of the material in question.

Cornyn asked Cole whether he believed a special prosecutor would be warranted to look into the cases at hand.

“I don’t believe that it would be necessary in this case, no,” Cole said.

Cornyn’s questioning today followed a lengthy and impassioned floor speech from Sen. John McCain (R-Ariz.) Tuesday in which he accused administration officials of leaking secret information for political gain “to paint a portrait of the president of the United States as a strong leader on national security issues.”

Today, White House spokesman Jay Carney responded to McCain’s allegations, saying, “We are not going to comment on any of the specific information contained in the articles referenced by Sen. McCain. This administration takes all appropriate and necessary steps to prevent leaks of classified information or sensitive information that could risk ongoing counterterrorism or intelligence operations. Any suggestion that this administration has authorized intentional leaks of classified information for political gain is grossly irresponsible.”

But McCain, the top Republican on the Senate Armed Services Committee and the 2008 Republican presidential nominee, has said that multiple leaks of classified material merited Congressional hearings and a special prosecutor to investigate whether federal law had been violated.

At McCain’s request, Senate Armed Services Chairman Carl Levin (D-Mich.) and Senate Intelligence Chairman Dianne Feinstein (D-Calif.) have agreed to hold hearings, potentially a joint session of their panels, to look into the matter.

“I am deeply disturbed by the continuing leaks of classified information to the media, most recently regarding alleged cyber efforts targeting Iran’s nuclear program,” Feinstein said in a statement Tuesday. “I sent a classified letter to the president outlining my deep concerns about the release of this information. I made it clear that disclosures of this type endanger American lives and undermine America’s national security.”