US President Barack Obama and Republican challenger Mitt Romney have faced each other in a combative debate that saw both men attack one another directly on a number of issues.
Snap polls after the debate pointed to a win for Obama, although it was by a narrower margin than Romney was said to have won the first encounter earlier this month.
Unlike his lackluster performance in that debate, the president was aggressive and fiery in the second, held on Tuesday at Hofstra University on Long Island, New York.
Romney, however, was just as spirited and the debate was tense and even personal at times. Many analysts say the race remains tight.
The discussion focused largely on domestic issues, though it covered a broader range of topics than the first presidential debate earlier this month.
From the economy to immigration and energy, Obama took a much more aggressive tone than in that previous debate, where he was widely criticised for giving long-winded answers and his reluctance to confront Romney.
The president went on the offensive early, saying in response to the first question that Romney’s economic plan would do little beyond cut taxes for wealthy Americans.
"Romney says he has a five-point plan. He doesn't have a five-point plan, he has a one-point plan," Obama said.
"And that’s to make sure folks at the top play by a different set of rules."
The president’s one-liner would set the tone for much of the first hour of debate, which used a "town hall" format, with questions coming from a pool of undecided voters in the audience.
One woman asked about taxes, and about Romney's plan to slash some of the "deductions" in the US tax code, which allow Americans to deduct items like mortgage interest from their taxable income.
Romney defended his tax and deficit numbers, saying 'of course they add up'
Romney has proposed a tax plan that could cut up to $5 trillion over the next 10 years, but would offset that lost revenue by reducing deductions and loopholes.
"I’m not going to have people at the high end pay less than they’re paying now... the top five per cent of taxpayers will continue to pay 60 per cent," Romney said. “And middle-income people are going to get a tax break."
But few economists believe that Romney could close the gap simply through cutting deductions, and Obama seized on that, accusing Romney of peddling false numbers.
"We haven’t heard from the governor any specifics beyond Big Bird and eliminating money for Planned Parenthood," Obama said, the former a reference to Romney's plan to slash federal funding for PBS, the public broadcaster. "The math doesn’t add up."
Romney responded testily, mentioning his business experience and his “25 years of balancing the budget."
"Of course they add up," he said of his tax figures.
'You’ll get your chance'
It is too early to tell what effect the debate will have on the candidates’ poll numbers. Obama’s lead narrowed sharply after his poor performance in the first debate: A four-point lead in an average of national polls shrank to just one point; some polls in crucial swing states showed Romney taking the lead.
Obama seemed determined to get under Romney’s skin, a tactic which seemed to work, leading to several other terse exchanges throughout the debate.
At one point, Romney interrupted the president, telling him "you’ll get your chance in a moment," a line which provoked an audible gasp from the audience. He also argued about the rules several times with the moderator, CNN anchor Candy Crowley, which prompted laughter from the audience.
The president took several opportunities to bring up Romney's positions from earlier this year, during the Republican primary, when he took sharply conservative views on many issues. He mentioned Romney's plan to encourage illegal immigrants to "self-deport," for example, and his refusal to consider any new gun control legislation.
One questioner asked what the candidates would do to ensure women have equal opportunities and receive equal pay for work. Obama told a familiar story about his grandmother and the "glass ceiling" she bumped into while working at a bank.
Romney told his own story, an anecdote about encouraging his staff to recruit female cabinet members during his term as governor of Massachusetts. "They brought me whole binders full of women," he said, presumably referring to women’s resumes.
The debate did briefly turn to foreign policy, for one question, about the attack last month on the US consulate in Benghazi which killed four people, including the ambassador, Christopher Stevens.
Watch the two candidates debate
the Benghazi consulate attack
Romney faulted the White House for its mixed messages in the aftermath of the attack; some officials said the attack was planned, while others suggested it was a spontaneous response to an anti-Islam video produced in the US.
The latter theory was debunked.
He also criticised the president for attending fundraisers in the days immediately after the attack.
"These actions taken by a president, and a leader, have symbolic significance," Romney said.
Romney claimed, wrongly, that it took Obama two weeks to label the assault a terrorist attack, a falsehood Crowley corrected; Obama described it as such the next morning, though other members of his administration contradicted that in the days that followed.
He criticised Romney for turning the deadly attack into a political issue. “That’s not how a commander-in-chief operates. You don’t turn national security into a political issue,” he said.