Boehner, an Ohio Republican, said the public should have access to emails a senior State Department official allegedly emailed her superiors after the 2011 attack to relay that she had told the Libyan ambassador the attack was conducted by Islamic terrorists.
"The State Department would not allow our committees to keep copies of this email when it was reviewed," Boehner said Thursday at a news conference. "And I would call on the president to order the State Department to release this email so that the American people can see it."
Boehner accused the White House of doing "everything possible to block access to the information that would outline the truth" surrounding possible security and intelligence failures in the attack on the consulate in which Ambassador Christopher Stevens and three other diplomatic staffers were killed.
Boehner is under increasing pressure to create a select committee to investigate the attack.
Rep. Frank Wolf, R-Va., in a letter to Boehner, said Wednesday's hearing "raised serious questions about the administration's efforts to respond to the Americans under fire at the annex in Benghazi," The Hill reported.
"What remains to be seen is whether the House will be complicit in that failure, or if we will pursue the truth -- wherever it may take us -- to ensure that we continue to deserve the sacrifices made by the men and women who serve our country."
Sen. John McCain, R-Ariz., said Wednesday's House hearing has increased the argument for a select committee." We need a full accounting, which can only come through a select committee in my view," McCain was quoted as saying.
Sen. Lindsey Graham, R-S.C., also backs the idea of a select committee.
"It's his decision to make, but we're making a big mistake by not doing a select committee," Graham said.
The Hill said almost 60 percent of the House Republican Conference supports Wolf's call for the committee.