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The new details mark the most information yet from an administration that has struggled to explain its decision-making before, during and after the attack.

While Mr. Obama made a single reference to terrorism in general in his comments from the White House Rose Garden on Sept. 12, the day after the attack, his administration pinned blame for the assault on a backlash to the video mocking Islam. The White House has said it was reflecting what the intelligence community had indicated and wasn’t trying to mislead the public.

Mr. Boehner, though, said there are inconsistencies between what the administration said in the weeks after the attack and what it appears to have known based on internal emails that were obtained and released by the oversight committee.

“No one in your administration can substitute for your authority and voice to explain to the American people the strategy and policies you directed during and in the aftermath of the terrorist attack,” the speaker wrote.

The White House didn’t respond to a request for comment, but Rep. Elijah E. Cummings of Maryland, the ranking Democrat on the oversight committee, said Republicans have distorted their investigation and misconstrued the significance of some of the emails they have obtained.

“It’s time to stop shamelessly politicizing this tragedy and let the independent investigation complete its work without interference,” he said.

Some Democrats have questioned Mr. Obama’s handling of the Libyan attack, but they have tried to avoid letting it damage his political prospects ahead of the Nov. 6 election.

The Senate Select Committee on Intelligence, led by Sen. Dianne Feinstein, California Democrat, has announced that it will hold hearings to try to get to the bottom of the situation — though they won’t begin until mid-November, or after the election.

That drew criticism from Senate Republicans.

“The truth is this hearing should have been held weeks ago,” said Sen. Marco Rubio, Florida Republican. “By the time it takes place, two full months will have passed since the Sept. 11 terrorist attack on our consulate in Libya. That’s way too long for the Senate to ask the important questions that have been building up.”

Meanwhile, Charles Woods, the father of one of the former Navy SEALs killed in the attack, called into the Lars Larson radio show this week to say he is still waiting for answers about what the White House knew.

He also said he wasn’t satisfied with the president’s apology when they met at Andrews Air Force Base, where the four bodies were returned to the U.S.

“It was not a sincere ‘I’m really sorry that your son died.’ But it was a totally insincere — more of a whining type — ‘I’m sorry.’ And it was like just shaking hands with a dead fish,” he said. “It just didn’t feel right.”