Mitt Romney has all but abandoned his fellow Republicans' efforts to use the terrorist attacks in Libya to raise questions about President Obama's policies and truthfulness.

Republicans have been pressing the White House about the killing of four Americans on Sept. 11 in Benghazi, questioning why the president took so long to acknowledge it was a terrorist attack. Romney took up that argument on the campaign trail, hitting Obama repeatedly on his handling of the episode.

But Romney abruptly dropped the issue entirely while debating foreign policy with Obama on Monday night. Romney's aides said the strategy shift is intended to help the Republican challenger look more presidential.

Instead of arguing over Libya, an issue on which Romney has already stumbled publicly, the Republican will focus on the broader repercussions of Obama's first-term policies, which he says left the U.S. less secure.

"The multiple failures surrounding the attack in Benghazi were symptomatic of the larger strategic failure in the region on the part of the Obama administration," a Romney campaign official told The Washington Examiner. "Gov. Romney spoke to that larger failure and made clear that he understood the serious threat of Islamic jihadism in the greater Middle East and North Africa."

For weeks, Romney and Republicans sounded the drumbeat that the Obama administration failed to properly secure the U.S. consulate in Libya. In particular, they questioned why the president refused to acknowledge that the strike was a coordinated terrorist attack. For two weeks, the White House insisted the strike was a spontaneous, violent response to an American-made anti-Islam video.

Now, Romney is speaking broadly about national security. At a campaign stop in Nevada on Tuesday, he vowed to "protect our military and keep it second to none in the world," before pivoting back to hammer Obama for his stewardship of a stagnant economy.

The shifting rhetoric is deliberate, Romney aides said. The Republican nominee is more interested in looking presidential than in scoring political points against an incumbent in a tightening race.

There were early indications that the shift is paying off. Romney still trails Obama on national security issues in polls, but after the debate, an increasing number of voters said they can envision Romney as a successful commander in chief.

Romney's abrupt dropping of the Libya issue surprised political observers, who say the tactical change carries risks.

"I think he takes somewhat of a hit with his base. I think they believe he should have drawn starker contrasts with the president," said David Makovsky, of the Washington Institute for Near East Policy. "Romney was not out to win [the debate] as much as was to persuade women he was not George W. Bush."

Republicans on Capitol Hill said Romney's debate strategy would not dissuade Rep. Darrell Issa, R-Calif., and other conservative lawmakers from continuing to press the Obama administration on the Libya attack.

But some GOP strategists give Romney credit for setting aside an issue with which he's struggled.

"People have already moved on from the last debate," said a top Republican consultant unaffiliated with the Romney campaign. "And Romney has fumbled this issue multiple times. There is no need for another self-inflicted wound. He's so much stronger on the economy -- and that's what voters care about."