A clutch of newly released White House emails provides the clearest evidence to date that top presidential aides sought to use anti-American protests sweeping across the Middle East in 2012 — as well as the aftermath of the Benghazi terrorist attack — to push an image of President Obama’s foreign policy as “steady and statesmanlike,” just weeks before his re-election. In one of the emails — written just hours after a top CIA official warned the White House that the Benghazi attack might not have been inspired by the Internet video that had triggered protests in Egypt, Yemen and other...