HEMPSTEAD, N.Y. - President Obama and Mitt Romney engaged Tuesday in one of the most intensive clashes in a televised presidential debate, with tensions between them spilling out in interruptions, personal rebukes and accusations of lying as they parried over the last four years under Obama and what the next four would look like under a President Romney.

Competing for a shrinking sliver of undecided voters, many of them women, their engagements at times bordered on physical as they circled each other or bounded out of their seats while the other was speaking, at times more intent to argue than to address the questions over jobs, taxes, energy, immigration and a range of other issues.

Obama, criticized for a lackluster debate performance two weeks ago, this time pressed an attack that allowed him to often dictate the terms of the debate, though an unbowed Romney met him every time. His broadsides started with a critique of Romney for his opposition to his administration's automobile bailout in his first answer -- "Gov. Romney said we should let Detroit go bankrupt" -- and ended more than 90 minutes later with an attack on Romney's secretly taped comments about the "47 percent" of Americans who he said did not take responsibility for their own lives. "When he said behind closed doors that 47 percent of the country considers themselves victims who refuse personal responsibility -- think about who he was talking about," Obama said at the end of the debate at Hofstra University in Hempstead, N.Y.

Romney stayed acutely focused on Obama's record in the face of it all, saying that the president had failed to deliver what he promised in his 2008 campaign and arguing repeatedly and strenuously, "We just can't afford four more years like the last four years."

He credited Obama for being "great as a speaker and describing his vision." But then he brought down the ultimate hammer in a challenge to an incumbent: "That's wonderful, except we have a record to look at."

The two took pains to fashion their arguments toward female voters. Obama mentioned Romney's vow to cut government funding for Planned Parenthood at least four times; Romney sought to soften his image, saying: "Every woman in America should have access to contraceptives."

The two men repeatedly rose from their stools, addressing one another as they moved around the stage. The men circled one another -- closer and closer -- as their voices grew sharper and louder in combative verbal exchanges. They talked over each other as they discussed issues like domestic energy production, jobs and taxes.

"What you're saying is just not true," Obama said.

"You'll get your chance in a moment; I'm still speaking," Romney said at one point, growing testy as the president tried to interject, drawing a gasp from the audience."

While the debate focused on policy differences, there was one more-personal moment, when Obama said Romney had investments in China.

"Mr. President, have you looked at your pension?" Romney interrupted.

"You know, I don't look at my pension. It's not as big as yours," Obama told his wealthier rival.

While Romney was on the defensive for much of the debate, his arguments were built around a theme he returned to again and again: the Obama administration's record and its failure to restart the economy. He used a litany of statistics to make his case. At least a half-dozen times, he said that 23 million Americans are out of work. And he said that 580,000 women had lost jobs in the last four years. "The president has tried, but his policies haven't worked," he said.

At other moments the verbal sparring took on a deeper, emotional resonance, such as when Romney suggested that the administration was intentionally misleading in its shifting explanations for the attack on the U.S. mission in Libya that resulted in the deaths of the U.S. ambassador, J. Christopher Stevens, and three other Americans.

"The suggestion that anybody in my team, whether the secretary of state, our U.N. ambassador, anybody on my team would play politics or mislead when we've lost four of our own, Governor, is offensive," Obama said. "That's not what we do. That's not what I do as president."

Obama noted that he had gone to the Rose Garden the day after the attack to say "this was an act of terror."

Romney asserted that Obama had not said that until 14 days later, prompting the moderator, Candy Crowley of CNN, to interject, "He did in fact, sir." Obama, interjected with a hint of anger, "Can you say that a little louder, Candy?"

Secretary of State Hillary Clinton has taken responsibility for the deaths, but Obama said bluntly, "I'm the president, and I'm always responsible."

The Associated Press contributed to this report.