With two weeks left before election day, the debate strayed frequently into domestic policy, with Romney seeking to bolster his argument that Obama had bungled the US economic recovery.

Running neck and neck in polls, neither man threw a knockout punch or made a noticeable gaffe as they clashed over Israel, Iran, Russia and the size of the US Navy.

While tamer than the second debate last week, the match-up had its share of zingers and putdowns, most of them doled out by an aggressive president eager to stop a surge in polls by the former Massachusetts governor.

"I know you haven't been in a position to actually execute foreign policy, but every time you've offered an opinion, you've been wrong," said Obama.

"Attacking me is not an agenda," was Romney's frequent retort, alluding to Republican accusations that Obama had not laid out enough of a policy plan for a second term.

Snap polls declared Obama the winner, but 60% of people in a CNN survey said Romney was capable of being commander-in-chief.

A CBS News poll said 53% believed Obama won the debate, versus 23% for Romney and 24% calling it a draw. The CNN poll put Obama as the winner by eight percentage points.

As the campaign enters its decisive phase, polls show a tied race after Romney clawed back from a deficit by outduelling Obama in their first debate on October 3.

Monday's showdown was one last chance for the candidates to appeal to millions of voters watching on TV. Obama was the aggressor from start to finish.

He criticised Romney for lacking ideas on the Middle East, mocked his calls for more ships in the US military and accused him of wanting to bring the US back to a long-abandoned Cold War stance.

"On a whole range of issues, whether it's the Middle East, whether it's Afghanistan, whether it's Iraq, whether it's now Iran, you've been all over the map," Obama said.

He had a biting and perhaps condescending response when the Republican said the US Navy had fewer ships now than at any time since 1917 and needed more.

"Governor, we also have fewer horses and bayonets," Obama said, suggesting that Romney's worldview was obsolete.