Washington (CNN) -- House Oversight and Government Reform Committee Chairman Darrell Issa said Sunday that he could issue subpoenas to the Justice Department this week in connection to a now-discredited federal gunrunning operation.

Speaking on "Fox News Sunday," Issa said that he wants a better understanding of who knew what, when about Operation Fast and Furious.

"But more importantly, we have to understand at what level did the authorization really come?" he said.

"People at the top of (the) Justice (Department) were well briefed, knew about it and seemed to be the command and control and funding for this program."

The operation involved agents from the Bureau of Alcohol, Tobacco, Firearms and Explosives allowing illegal sales of guns believed to be destined for Mexican drug cartels to "walk" from Phoenix, Arizona, gun stores into Mexico.

The idea was to track the sellers and purchasers of guns to Mexican cartels, but the program became mired in controversy after weapons found at Mexican and American murder scenes were traced back to the program. Mexican officials and critics in the United States called the program a failure, saying it exacerbated the longstanding problem of U.S. weapons getting into the hands of the violent Mexican cartels.

U.S. Attorney General Eric Holder testified before the Judiciary Committee in May that he had known about the Fast and Furious program for just a few weeks.

He responded angrily Friday to Republican critics of his handling of the controversial operation, charging them with using "irresponsible and inflammatory rhetoric."

"I simply cannot sit idly by as a (Republican) member of the House Committee on Oversight and Government Reform suggests, as happened this week, that law enforcement and government employees who devote their lives to protecting our citizens be considered 'accessories to murder,'" Holder said in a letter to members of Congress.

"Such irresponsible and inflammatory rhetoric must be repudiated in the strongest possible terms," he said.

The bitter debate followed the release last week of Justice Department documents on Capitol Hill that prompted Republican critics to charge Holder knew about the now-discredited gun operation before he previously claimed.

Holder insisted, as his Justice Department aides have for several days, that he was not inconsistent in his testimony.

At the committee's May 3 hearing, Issa, R-California, raised the subject of the program with Holder.

"When did you first know about the program, officially, I believe, called Fast and Furious? To the best of your knowledge, what date?" Issa asked.

"I'm not sure of the exact date, but I probably heard about Operation Fast and Furious for the first time over the past few weeks," Holder testified.

On Sunday, Issa told "Fox News Sunday" that the Judiciary Committee has invited Holder to "come and clear the record."

"Clearly, he knew when he said he didn't know. Now the question is what did he know and how is he going to explain why he gave that answer," said Issa.