Some Republicans view the attack, in which militants killed four Americans at the U.S. mission in Benghazi including Ambassador Christopher Stevens, as a political liability that could hurt President Barack Obama's Democrats in November.
Although the issue may resonate with some voters, pushing it too hard is politically risky for Republicans, said Republican Senator Lindsey Graham of South Carolina, who is running for re-election this year.
"If we're playing politics with Benghazi, we'll get burned," Graham said on CBS's "Face the Nation."
When asked if the issue has become more about politics than substance, Graham said: "Anyone who believes this is just about politics, go tell that to the family members ... Anyone who plays politics with Benghazi will get burned."
The Benghazi issue resurfaced last week after a conservative watchdog group released emails that it said showed Obama administration officials were concerned with protecting the president's image in the days after the attack.
Republicans in the House of Representatives seized on the new evidence last week and called for a special, "select committee" of lawmakers to investigate.
In response, a State Department spokeswoman said on Friday: "This is just another attempt to use this politically."
Renewed attention on the Benghazi attack could raise political trouble for Hillary Clinton, a possible 2016 Democratic presidential candidate, who was secretary of state during Obama's first term and at the time of the attack.
In a May 2 interview with Reuters, Republican Senator Charles Grassley said the Benghazi attack was among a series of scandals that highlighted concerns about Obama overstepping its authority and which would be on the minds of voters in November.