Correction: An earlier version of this article misidentified the union that represents Foreign Service officers. It is the American Foreign Service Association, not the Association of Foreign Service Officers. The article also erred in describing Gregory Hicks as part of a slate of candidates endorsed by the association’s leadership. Hicks, one of two vice-presidential candidates seeking to represent Foreign Service officers at the State Department, is on the only slate of candidates running, but the leadership makes no endorsements.

In this Thursday, Sept. 13, 2012 file photo, a Libyan man investigates the inside of the U.S. Consulate after an attack that killed four Americans, including Ambassador Chris Stevens, on the night of Tuesday, Sept. 11, 2012, in Benghazi, Libya. (Mohammad Hannon/AP)

House Speaker John A. Boehner said Thursday that the American public should be allowed to see internal administration e-mails related to September’s terrorist attack in Benghazi, Libya, and called on President Obama to release them.

The e-mails, which are available to Congress with restrictions on their release, include one that Republican lawmakers said this week proved that the administration tried to cover up its belief that the Sept. 11 assault was terrorism and not, as it initially and erroneously claimed, an anti-American protest that got out of hand.

Boehner’s comments, and GOP calls for new investigations the day after a House hearing on the subject, indicated that Republicans are far from ready to abandon charges of administration wrongdoing before, during and after the attack, which killed four Americans.

The State Department quickly countered that Boehner and Rep. Trey Gowdy (R-S.C.), who first brought it up at the hearing, misstated the contents of a Sept. 12 e-mail from Acting Assistant Secretary Elizabeth Jones to her superiors. Jones, Boehner said, wrote that “she told the Libyan ambassador that the attack was conducted by Islamic terrorists.”

State Department spokesman Patrick Ventrell said Jones had not used the word “terrorists” but had called the perpetrators “extremists.” It was unclear whether he considered that a substantive difference or a distinction. He said there was a standard “redaction process” for any publicly released documents.

The House Oversight and Government Reform Committee holds a hearing about last year's deadly assault on the U.S. diplomatic mission in Benghazi, Libya, on Capitol Hill in Washington, Wednesday, May 8, 2013. (J. Scott Applewhite/AP)

Ventrell repeated the administration’s insistence that the description of the attack as the response to an offensive video sparking protests across the Islamic world that day — a view most prominently offered in television interviews by Susan E. Rice, the U.S. ambassador to the United Nations, days later — was the consensus of the U.S. intelligence community.

The hearing, including a riveting account of the night of the attack by Gregory Hicks, who was deputy ambassador at the embassy in Tripoli, largely concentrated on questions addressed by officials in extensive testimony over the past six months. But at least three aspects sparked new rounds of questions.

Hicks testified that a four-man unit of Special Operations military personnel on temporary duty in Tripoli, the Libyan capital, had tried to go to Benghazi that night to help with a rescue effort before superiors told them to stand down.

Pentagon spokesman George Little said the order came from the Special Operations component of the Africa Command, based in Germany, which concluded that the four were more urgently needed in Tripoli, where the embassy was being evacuated, and could not get to Benghazi in time to make a difference.

As the State Department struggled to respond to Hicks’s allegations without appearing to criticize a colleague who performed valiantly during that traumatic night in Libya, officials questioned his account of why U.S. Ambassador J. Christopher Stevens, who was among those killed, was in Benghazi in the first place.

Hicks said then-Secretary of State Hillary Rodham Clinton intended to make the temporary outpost into a permanent U.S. installation and had instructed Stevens to travel there before Sept. 30, the end of the fiscal year.

Officials who spoke on the condition of anonymity to discuss internal department deliberations said funding for the facility was approved through the end of 2012. Although Clinton and Stevens were committed to an ongoing presence in Benghazi, they said, no such orders were given to Stevens, adding that the review task that Hicks described would have been done by security and building specialists, not the ambassador. Instead, Stevens had gone to attend a cultural event and to renew contacts from an earlier posting there.

Hicks also said he had been demoted for privately and publicly questioning administration actions and statements during and after the attack and for talking to a Republican lawmaker investigating it.

After what he described as a stellar career, he said that his “management style” was questioned and that he was made to feel uncomfortable. He voluntarily gave up his Libya assignment, he said, and was “demoted” to a desk job in Washington.

Subsequent requests for another high-level post have been rejected, Hicks’s attorney, Victoria Toensing, said in an interview, amounting to hints that he was “better off resigning.”

In a news conference in Rome on Thursday, Secretary of State John F. Kerry said he has seen only “cursory” accounts of the hearing and that it would be inappropriate to comment on the specifics. But, he said, “the State Department will leave no stone unturned” in responding to congressional inquiries.

Ventrell denied any retaliation, saying that Hicks’s departure from Libya was between regular department assignment cycles and that he is welcome to bid on upcoming jobs.

Some current and former colleagues noted that the State Department has at times been unfriendly to dissidents. But they questioned Hicks’s portrayal of his status. Hicks is an “FS-1,” a grade equivalent to a colonel in the military. As in the military, his failure to rise above that grade after 22 years in the Foreign Service would limit his options.

Despite indicating that he is seeking another overseas post, Hicks is the favored candidate to become vice president of the Foreign Service union.

Results, including ballots from those overseas, are due in June. The job, which includes serving as the chief negotiator for members within the State Department, is the full-time equivalent of a two-year Foreign Service assignment.

Anne Gearan in Rome contributed to this report.