Newly-released emails from within the White House shed more light on the way the administration shaped its response to the 2012 attack in Benghazi, Libya that left four Americans dead.

Obtained by the conservative watchdog group Judicial Watch through a Freedom of Information Act request, an email from then-White House Deputy Strategic Communications Adviser Ben Rhodes (the brother of CBS News president David Rhodes) listed several goals for then-United Nations Ambassador Susan Rice as she prepared to go on political talk shows just a few days after the Sept. 11, 2012 attack.

Rhodes wrote that one "goal" for Rice was "To underscore that these protests are rooted in and Internet video, and not a broader failure or policy." Another stated "goal" was to "reinforce the President and Administration's strength."

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Congressional Republicans say the new email shows a deliberate attempt by the White House to put politics ahead of the facts in the weeks before President Obama's re-election.

"It demonstrates for the first time that the direction on the talking points came directly out of the White House," Rep. Jason Chaffetz, R-Utah, told CBS This Morning.

Sen. Lindsey Graham, R-S.C., told Newsmax that the emails amounted to a "smoking gun."

"It shows political operatives in the White House working to create a political narrative at odds with the facts," he said.

White House spokesman Jay Carney on Wednesday said that the recommendations from Rhodes "were not about Benghazi" specifically, but "about the general situation in the Muslim world... where you saw protests outside of embassy facilities across the region."

Carney stressed that it was the CIA -- not the White House -- that prepared talking points on Benghazi. Those talking points were prepared at the request of Congress, and the White House decided that Rice would use those talking points for the sake of consistency.

"We believed that it was appropriate for everyone... to be using the same set of points produced by the intelligence community," Carney said.

Internal emails the White House released last year showed how the CIA modified its Benghazi talking points repeatedly before Rice appeared on five political talk shows on Sept. 16, 2012. The final version of the talking points said the attack may have been "spontaneously inspired by the protests at the U.S. embassy in Cairo." One page of the documents released showed handwritten changes ordered by Mike Morell, former deputy director of the CIA and a current CBS News contributor. In his congressional testimony earlier this month, Morell said an intelligence analyst said on Sept. 13, 2012 that the attack evolved spontaneously from a protest.

A national security council spokesman told CBS News that the latest email from Rhodes simply "contains general topline talking points."

"There were protests taking place across the region in reaction to an offensive internet video, so that's what these points addressed," the spokesperson said.

Congress, meanwhile, is still actively investigating the matter.

On Thursday. the House Oversight and Government Reform Committee will hold a hearing called, "Benghazi, Instability, and a New Government: Successes and Failures of U.S. Intervention in Libya." Earlier this week, a trio of Republican senators called on the House and Senate Foreign Affairs Committees to hold more hearings.