Barack Obama and his challenger Mitt Romney have battled over national security in the third and final presidential debate at Boca Raton, Florida.

The rivals tangled over the Arab Spring, Iran, China’s rise and more in a feisty 90-minute head-to-head.

Barack Obama said his Republican challenger was “all over the map” on foreign policy, while Mitt Romney said the president had failed to uphold American global leadership.

The two candidates are running neck and neck with two weeks until the election.

In the final debate, moderated by veteran CBS News presenter Bob Schieffer, there were no noticeable gaffes or knockout blows.

The forum at Lynn University featured little of the interrupting that marked their second encounter last week in New York, when Barack Obama came out swinging after his lackluster performance in their first head to head in Denver, Colorado.

The rivals found some common ground – each declared unequivocal support for Israel and both voiced opposition to US military involvement in Syria.

Mitt Romney also said he agreed with the president’s policy of withdrawing troops from Afghanistan by 2014 – the Republican has suggested otherwise in the past.

In laying out one of his overarching themes on foreign policy, Mitt Romney said the US under President Barack Obama’s leadership had allowed “tumult” to engulf the Middle East.

He cited civilian deaths in Syria, the rise of al-Qaeda affiliates in North Africa and Iran’s nuclear programme.

But the Republican steered clear of his suggestion in the last debate that the Obama administration had mishandled last month’s Libya US consulate attack, which left four Americans dead.

Barack Obama and his challenger Mitt Romney have battled over national security in the third and final presidential debate at Boca Raton

“What’s been happening over the last couple of years is, as we’re watching this tumult in the Middle East, this rising tide of chaos occur, you see al-Qaeda rushing in, you see other jihadist groups rushing in,” Mitt Romney said.

“I congratulate him on taking out Osama Bin Laden and taking on the leadership of al-Qaeda, but we can’t kill our way out of this… We must have a comprehensive strategy.”

Barack Obama hit back that he was glad that Mitt Romney had recognized the threat posed by al-Qaeda, reminding the former Massachusetts governor that he had earlier this year cast Russia as America’s number one geo-political foe.

The president sought to portray Mitt Romney as a foreign policy novice who lacked the consistency needed to be commander-in-chief.

Barack Obama said Mitt Romney had backed a continued troop presence in Iraq, opposed nuclear treaties with Russia, even when they had broad bipartisan backing, and accused the Republican of flip-flopping over whether the US should have a timeline for leaving Afghanistan.

“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,” Barack Obama said.

The president said that he had ended the war in Iraq and “decimated” al-Qaeda’s leadership, allowing the US to prepare a responsible timeline for withdrawing from Afghanistan.

Mitt Romney, whose book is called No Apology, accused Barack Obama of having gone on “an apology tour” after he took office and of saying at the time he would meet “all the world’s worst actors”, including leaders from North Korea and Iran.

“I think they looked at that and saw weakness,” Mitt Romney said.

The president hit back, saying: “Nothing Governor Romney has just said is true, starting with the notion of me apologizing,” a claim Barack Obama labeled the “biggest whopper” of the campaign.

The rivals also jostled to act tougher than the other on China, as allegations flew about trade violations and currency manipulation by Beijing.

Although the debate’s focus was meant to be on foreign affairs, the two candidates pivoted repeatedly back to the fragile US economy, the issue uppermost in voters’ minds.

Mitt Romney said he knew what it took to create jobs and boost pay, while Barack Obama was nine million jobs short of his pledge of 5.4% employment.

But Barack Obama accused Mitt Romney of planning $5 trillion of tax cuts and $2 trillion of defence spending the military had not even requested.

“You mentioned the Navy, for example, and that we have fewer ships than we did in 1916,” Barack Obama said in one of the night’s most memorable lines.

“Well, governor, we also have fewer horses and bayonets, because the nature of our military’s changed.”

An NBC poll on Sunday put the men in a dead heat, each with 47% support.

A lackluster performance by Barack Obama in the opening debate in Denver, Colorado, on 3 October gave Mitt Romney a campaign boost.

But in their second face-off in New York last week, a more aggressive Barack Obama buried the memory of a poor first showing as he came out swinging on the economy, tax and foreign policy.

After Monday night’s showdown, both candidates will be returning to the campaign trail for a grueling final two weeks of wooing voters in swing states.

The final debate behind them, both men will now launch a final fortnight of campaigning. Already four million ballots have been cast in early voting in more than two dozen states.

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