During the tense encounter in Florida, the rivals tangled over the Arab Spring, Iran, Israel and China.

Mr Obama said his rival was "all over the map" on foreign policy. But Mr Romney said the president had allowed "chaos" to engulf the Middle East.

Two instant polls said Mr Obama won the head to head.

'Rising tide of chaos'

The Democratic president went on the attack from the start of Monday night's forum, trying to trip up his rival.

But analysts say Mr Obama did not land any knockout blows on Mr Romney, who has been gathering momentum with two weeks to go until election day, in a race that is now neck and neck.

The debate at Lynn University in Boca Raton, which was moderated by veteran CBS News presenter Bob Schieffer, was not as fractious as their second encounter last week, when Mr Obama came out fighting after his lethargic performance in their first meeting.

But there were several scathing exchanges, with the president seeking to portray his challenger as a foreign policy novice who lacked the consistency to be commander-in-chief.

Mr Obama said the former Massachusetts governor had backed a continued troop presence in Iraq, opposed nuclear treaties with Russia and flip-flopped over when the US should leave 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," said Mr Obama.

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