House Republicans accused the Obama administration Thursday of “perhaps criminal” behavior for having withheld for months key email that sheds light on how the administration framed its post-Benghazi talking points, potentially violating a congressional subpoena.

House Speaker John A. Boehner, Ohio Republican, said Secretary of State John F. Kerry will have to come before Congress to explain why his department refused to release the email until forced to do so by a judge.

Meanwhile, a retired Air Force brigadier general who was in the U.S. Africa Command’s headquarters the night of the 2012 attack on the American diplomatic post in Benghazi testified that he and others quickly realized the assault was spawned by terrorists. The general said it was either negligence or willful ignorance that led the White House, amid a re-election campaign, to say the violence was ignited by anger over a video.

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Several high-profile Republican senators said the revelations, combined with questions still unanswered, should spur Congress to create an independent investigative committee to get the answers.

“If the White House won’t explain it, Secretary Kerry should come to the Capitol to explain why he defied an official congressional subpoena. And the White House needs to understand that this investigation will not end until the entire truth is revealed and justice and accountability are served,” Mr. Boehner said.

Judicial Watch, a public interest law firm, obtained the email under an open-records request enforced by a court order. The email shows a top White House national security official shaping how U.N. Ambassador Susan E. Rice should talk about the attack on a round of Sunday political talk shows. The email said blame should be placed on an Internet video.

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The White House dismissed the rekindled questions.

“This is a conspiracy theory in search of a conspiracy,” press secretary Jay Carney said.

But he altered his explanation from Wednesday, when he said the reason the email wasn’t turned over in response to requests was that it wasn’t about Benghazi. Instead, Mr. Carney said it was a State Department decision and Mr. Kerry’s department would have to provide the answers.

Mr. Carney did acknowledge Thursday that the email mentioned Benghazi once, in a question about how administration officials should respond to a report in a British newspaper that the U.S. ignored a warning 48 hours before the attack.

Mr. Carney said Republicans in Congress should drop the Benghazi investigation and instead focus on the economy. He also said the president is focused on finding the perpetrators who killed four Americans in Benghazi.

“If anyone doubts that, they should ask … any friends and family members of Osama bin Laden,” Mr. Carney said.

Republicans in Congress counter that Mr. Obama also promised to bring the perpetrators of the Benghazi attack to justice, yet nobody has been apprehended more than 18 months later. The government has secured a sealed indictment in federal court that reportedly names a number of suspects including Ahmed Abu Khattalah, the founder of Ansar al-Sharia.

Immediately after the attack, the Obama administration said it was a mob protest spawned by an Internet video mocking Islam. Such a protest broke out in Cairo on Sept. 11, 2012.

But Republicans said the CIA, the Defense Department and parts of the State Department quickly realized that the Benghazi attack was not a protest. They question why the White House deployed Ms. Rice to the talk shows nearly a week later to repeat that message.

Rep. Darrell E. Issa, California Republican and the House’s top investigator of Benghazi, said Thursday that it was “perhaps criminal” of the Obama administration to withhold the email.

“The facts are coming out that this administration has knowingly withheld documents pursuant to congressional subpoenas,” Mr. Issa said as he opened a hearing into the administration’s handling of the deadly attack, which killed U.S. Ambassador J. Christopher Stevens and three other Americans.

Testifying at the hearing was Brig. Gen. Robert Lovell, who was overseeing intelligence for Africom the night of the attack and said the military knew early on that the violence wasn’t about a video.

He also said the decision not to respond with military action likely was made outside of the Defense Department. He said the military was waiting on a request from the State Department — a request that never came.

“Basically, there was a lot of looking to the State Department for what they wanted and the deference to the Libyan people and the sense of deference to the desires of the State Department in terms of what they would like to have,” the general testified.

House Armed Services Committee Chairman Howard P. “Buck” McKeon, California Republican, said Gen. Lovell’s role didn’t give him reliable insight into the scope of options available to commanders.

“The Armed Services Committee has interviewed more than a dozen witnesses in the operational chain of command that night, yielding thousands of pages of transcripts, e-mails, and other documents. We have no evidence that Department of State officials delayed the decision to deploy what few resources DoD had available to respond,” Mr. McKeon said in a statement.