President Obama used an hour-long town hall event here Monday to mock Republican Mitt Romney’s economic plan as one that would create jobs only overseas, as the two candidates continued to trade insults in a presidential campaign that has turned increasingly bitter in recent days.

Speaking at the Cincinnati Music Hall, Obama cited a new study that found that Romney’s support of a territorial tax system — in which U.S. companies are not taxed on their overseas profits — would create 800,000 jobs outside the country.

“There’s only one problem: The jobs wouldn’t be in America,” Obama told 1,200 supporters, referring to the report in Tax Notes, a nonprofit, nonpartisan publication.

Obama, who has proposed tax breaks for companies that bring jobs back to the United States, added that “we don’t need a president who plans to ship more jobs overseas.”

The president’s latest broadside aimed to keep Romney on the defensive over accusations that he supported the practice of offshoring jobs while he oversaw Bain Capital, a private equity firm. Those charges, which Romney disputes, have allowed Obama to shift the focus of the debate from the sluggish economy to his rival’s record in the private sector and have ramped up GOP pressure on the former Massachusetts governor to mount an effective rebuttal.

Republicans dismissed the Tax Notes report, pointing out that members of Obama’s jobs council have supported a territorial tax as a way to stimulate economic growth.

Speaking to reporters in Baton Rouge, where Romney was appearing at an intimate fundraiser, senior campaign adviser Eric Fehrnstrom lashed out at the Obama campaign, likening it to a “bottomless pit.”

“Every day, they reach a new low,” he said. “When you hear a false and dishonest attack from the Obama campaign, ask yourself this question: What does this have to do with creating more jobs?”

Romney has defended himself by insisting that Bain did not invest in companies that sent jobs abroad until after he gave up daily management of the company in 1999. But the Obama campaign has seized on media reports that Bain continued to list Romney as chief executive three years later on filings to the Securities and Exchange Commission.

Romney said in Louisiana on Monday that he would not “apologize for being a successful businessman” in the face of the attacks.

“Those who take risks sometimes succeed brilliantly, wonderfully, and that makes us a stronger economy,” he said.

Romney’s campaign distributed a memo Monday morning that suggested that the Bain attacks were falling flat, not affecting polling even as Obama has heavily outspent his rival on television ads in swing states.

“There is no evidence to suggest that the ballot has moved,” Neil Newhouse, Romney’s pollster, wrote in the memo. “If throwing the kitchen sink at Gov. Romney while leveraging a two-to-one ad-spending advantage doesn’t move numbers for the President, that’s got to tell you something about the state of the electorate: Voters are frustrated with President Obama’s failure to keep his promises from the 2008 campaign.”

The president’s latest broadside also drew an angry response from Romney’s Republican allies on Capitol Hill. GOP aides distributed an article by the conservative Weekly Standard that said the Tax Notes report was prepared by a professor at Reed College in Portland, Ore., who has donated exclusively to Obama and Democrats.

That disclosure played directly into the hands of the Romney camp, which on Monday tried to move past the Bain debate by launching a new offensive against Obama for what it called “crony capitalism.”

Speaking to about 40 donors at his fundraising event, Romney again raised the example of Fisker Automotive, a California manufacturer of hybrid electric cars that has received government loans and recently laid off some workers. The company’s investors include a firm that counts former Democratic vice president Al Gore as a partner.

“It is taking your tax dollars and putting it in businesses owned by contributors to his campaign, and that is smelly at best. It stinks,” Romney told his supporters.

Obama’s trip to Cincinnati came just 10 days after he wrapped up a two-day tour of Ohio, considered a crucial bellwether for both campaigns.

Although both sides think the race will be tight, polls show Obama holding a small but steady advantage in Ohio and other swing states. His campaign has outspent Romney by $91 million to $23 million on television ads in those battlegrounds.

Romney, who also has made several appearances in the state, will return to Ohio for a campaign event Wednesday.

Nakamura reported from Washington.