Poll: Who won the final presidential debate?

(CNN) — President Barack Obama quickly struck out at Mitt Romney’s foreign policy inexperience during Monday’s presidential debate, with the Republican nominee defending his positions and promoting what he described as a thoughtful and comprehensive strategy to combat extremism.

The third and final face-to-face showdown occurred with the candidates neck-and-neck in national polls with 15 days until Election Day, and the race hinging on a handful of battleground states — particularly Ohio, Florida and Virginia.

According to the latest polls, Obama has a slight lead in Ohio. Romney is ahead in Florida and Virginia is a dead heat.

The former Massachusetts governor fielded the first question, on Libya, where extremists attacked the U.S. diplomatic mission in Benghazi on September 11 and killed four Americans. 

Romney applauded Obama’s efforts to kill Osama bin Laden and other al Qaeda leaders but insisted that “we can’t kill our way of this mess.” Rather, he pushed for “a comprehensive strategy” to curb violent extremism in the Middle East.

“The key is the pathway is to get the Muslim world to reject extremism on its own,” Romney said, proposing U.S. policies to promote economic development, better education, gender equity and helping create institutions.

Obama responded sharply. He criticized his opponent on a host of foreign policy issues — claiming Romney had favored positions that would have hurt the United States or offered sometimes contradictory views.

“What we need to do with respect to the Middle East is strong, steady leadership — not wrong and reckless leadership that is all over the map,” the president said.

Obama more than once sought to highlight Romney’s lack of foreign policy experience, while Romney said Obama’s foreign affairs policies have made the United States less respected and more vulnerable.

The candidates were at odds as well about how Washington should ultimately respond to the civil war in Syria. [BONUS: Check out the Political IQ’s Video Matrix]

Talking about the need to provide those fighting Syrian President Bashar al-Assad’s forces with arms, Romney said the Democratic incumbent has not enough to curb violence that has left tens of thousands of people dead and also destabilized the region.

“We should be playing the leadership role,” Romney said.

That precipitated a quick response from Obama, who pointed to American efforts to organize international efforts to address the issue as well as its support for opposition factions. “We are making sure that those we help will be our friends (in the future),” he said.

A strong performance by Romney against a lackluster Obama in the first debate October 3 in Denver helped the GOP challenger tighten the race and even pass the president in some polls.

The president fought back to win the second debate last week in New York, according to polls and pundits, setting up the Monday’s night showdown at Lynn University in Boca Raton, Florida, moderated by CBS News Chief Washington Correspondent Bob Schieffer.

Until recently, polls showed Obama ahead of the former governor on foreign relations issues, and the Romney campaign has mounted pointed attacks in an attempt to narrow the president’s advantage.

Other issues to be discussed in the debate included Iran’s nuclear ambitions, China and the war in Afghanistan.

Romney has landed blows thus far in the campaign by arguing that continued high unemployment and sluggish growth showed failed policies under the president, while promoting his own business background.

In a major foreign policy address on October 8, Romney promoted a traditional U.S. foreign policy dating back decades, based on exerting global influence through military and economic power. While the speech sought to distinguish himself from Obama on foreign policy, specific proposals he cited then were similar to what the administration is doing.

Obama’s campaign has accused Romney of shifting positions on foreign policy matters and mishandling a trip to England, Israel and Poland this summer when he publicly questioned London’s preparedness to host the Olympic Games and cited cultural differences as a reason for economic disparities between Israelis and Palestinians.