Clinton but did not pose any questions because it had established the facts to its satisfaction and concluded that mistakes were made by less senior officials. Likewise, he said, the panel did not question her two deputies.

“We had plenty of opportunity had we felt it was necessary, all five of us, to ask them questions,” Mr. Pickering said in a round of network television interviews intended to explain his work. “We didn’t believe that was necessary, and I don’t see any reason to do so now.”

By the time they talked with her, he added, “we had questioned people who had attended meetings with her” and “I don’t think that there was anything there that we didn’t know.”

The board’s review of the attack in Benghazi has become a focus as Republican lawmakers investigate the Obama administration’s handling of the episode. The No. 2 diplomat in Libya at the time of the attack said in an interview with Congressional investigators that was disclosed last week that the review “let people off the hook,” and a State Department official testified that the board failed to interview “people who I personally know were involved in key decisions.”

Representative Darrell Issa, a California Republican and the chairman of the House Oversight and Government Reform Committee, said he would seek testimony from Mr. Pickering and his vice chairman, Adm. Mike Mullen, the retired chairman of the Joint Chiefs of Staff. “We’re going to want to go through at length how” the board “reached its conclusions, who it interviewed, and why we believe there are shortcomings,” Mr. Issa said on the NBC program “Meet the Press.”

The board’s report on the Sept. 11 attack that killed Ambassador J. Christopher Stevens and three other Americans offered harsh criticism of the State Department’s handling of security in Benghazi, citing “systemic failures and leadership and management deficiencies at senior levels.” But it did not attribute those to Mrs. Clinton, whose role or lack of role went unmentioned in the unclassified version of the report released in December.

Mr. Pickering’s appearances on CBS and NBC put the spotlight on him. He acknowledged that he was initially disinclined to testify before Congress because it seemed like a political circus but said he changed his mind and volunteered, only to be put off. That produced a quarrel on the set of the NBC studio, where he and Mr. Issa sat side by side.

“Ambassador Pickering, his people and he, refused to come before our committee,” Mr. Issa said.

Mr. Pickering interrupted. “That is not true,” he said.

“We have it in writing,” Mr. Issa countered, suggesting perhaps it was the White House that refused to let him appear.

“I said the day before the hearings I was willing to appear, to come to the very hearings he excluded me from,” Mr. Pickering said.

“Don’t tell me I excluded you,” Mr. Issa interjected.

“We were told the majority said I was not welcome at that hearing,” Mr. Pickering said. “I could come at some other time.”

Mr. Issa said he wanted to explore whether the panel interviewed enough witnesses and focused high enough in assigning responsibility. “Ultimately, if that got it right, then we can put this to a rest,” he said. “We believe it was insufficient.”

On the CBS News program “Face the Nation,” Mr. Pickering said there was no need. “I don’t see yet any reason why what we did at the accountability review board should be reopened,” he said.

Mrs. Clinton, who testified on Capitol Hill on Benghazi in January before stepping down, has said she takes responsibility as the leader of her department. Democrats say the renewed Republican focus on Benghazi in recent days is nothing more than an attempt to sully Mrs. Clinton, who is seen as the front-runner for her party’s presidential nomination in 2016.

“Unfortunately, this has been caught up in the 2016 presidential campaign, this effort to go after Hillary Clinton,” Senator Richard J. Durbin, Democrat of Illinois, said on CBS. “The reason she wasn’t interviewed – because she didn’t have any direct-line responsibility for the decisions that were made. But they want to bring her in because they think it’s a good political show.”

Mr. Issa denied that Mrs. Clinton or President Obama were targets of the investigation. But he accused the administration of deceiving the public by blaming the attack on an incendiary anti-Muslim video rather than on specific terrorist groups. “The American people were effectively lied to for a period of about a month,” he said. “They were in fact covering up an easy attack that succeeded, that was from the get-go really about a terrorist attack. It was never about a video.”

Senator John McCain, Republican of Arizona, called for a select committee to investigate, just as scores of House Republicans did last week. “I’d call it a cover-up,” he said on the ABC News program “This Week.” “I would call it a cover-up in the extent that there was willful removal of information which was obvious.”

Former Defense Secretary Robert M. Gates came to the assistance of the administration. Mr. Gates, who served several Republican presidents in various capacities before staying on under Mr. Obama for two and a half years, rebutted suggestions that the Pentagon could have scrambled jets or special forces during the attack, calling that a “cartoonish impression of military capabilities.”

“Frankly had I been in the job at the time, I think my decisions would have been just as theirs were,” he said on CBS. “Frankly, I’ve heard ‘Well, why didn’t you just fly a fighter jet over and try and scare ’em with the noise or something?’ Well, given the number of surface-to-air missiles that have disappeared from Qaddafi’s arsenals, I would not have approved sending an aircraft, a single aircraft, over Benghazi under those circumstances.”