WASHINGTON (Reuters) - President Barack Obama's campaign and top Democrats on Sunday called on Mitt Romney to release more personal tax records and raised questions about his offshore assets that the Republican challenger's campaign condemned as an "unseemly and disgusting" character assault.

Democrats and Republicans tussled over the economy, but it was Romney's offshore assets that Democrats seized on during the Sunday talk shows in their quest to portray him as a wealthy man out of touch with ordinary Americans. Romney faces Obama in the November 6 election and polls indicate a close race.

Democratic National Committee Chairwoman Debbie Wasserman Schultz raised the issue on "Fox News Sunday" as her interview time ran out.

"I'd really like to see Mitt Romney release more than one year of tax records, because there's been disturbing reports recently that he's got a Bermuda corporation, a secretive Bermuda corporation that no one knows anything about, investments in the Caymans, kind of Swiss bank account."

"Americans need to ask themselves why does an American businessman need a Swiss bank account and secretive investments like that?" Schultz said.

Obama campaign adviser Robert Gibbs, on CNN's "State of the Union," called on Romney to release years of back tax records to allow scrutiny of his adherence to tax law. Asked whether Romney had broken the law, Gibbs said, "Well, we don't know."

"The one thing he could do ... to clear up whether or not he's done anything illegal - whether he's shielding his income from taxes in Bermuda or Switzerland - is to do what every other presidential candidate's done, and that's to release a series of years of their own tax returns," Gibbs said.

"This is a guy whose slogan is: 'Believe in America' - and it should be 'Business in Bermuda.' That's what Mitt Romney's all about," Gibbs said.

Romney's campaign fought back.

"The Obama campaign's latest unfounded character assault on Mitt Romney is unseemly and disgusting," said Andrea Saul, a Romney campaign spokeswoman.

The Associated Press has reported that an offshore company based in Bermuda has helped bolster Romney's wealth even though it did not appear on his state or federal financial reports for 15 years.

The Obama campaign released an online video on Sunday raising questions about Romney's offshore accounts. "Mitt Romney could be the first president in history to stash millions offshore so the American people deserve an explanation as to why he chose to invest in other countries known as tax havens rather than the United States," the campaign said in a statement.

'DISHONEST ATTACKS'

Saul defended the Republican presidential challenger, saying, "Mitt Romney had a successful career in the private sector, pays every dime of taxes he owes, has given generously to charitable organizations, and served numerous causes greater than himself."

"Barack Obama has become what he once ran against - a typical politician willing to use false and dishonest attacks to save his job after failing to do his job," Saul said.

Romney, a multi-millionaire former private equity executive, is one of the richest men ever to run for U.S. president. He has an estimated net worth of up to $250 million.

Romney has released his 2010 returns and estimates for 2011 but has been reluctant to release more. In April, he requested an extension to file his 2011 tax forms while estimating his tax liability at $3.2 million for last year.

Four months before the presidential election, Democrats are seeking to portray Romney as out of touch with the plight of Americans in a struggling economy, while Republicans point to Obama's policies as inadequate for strong economic growth.

The latest data point in the political battle over which candidate is better for the U.S. economy was the June U.S. employment report on Friday that showed non-farm payrolls grew by 80,000 jobs and the unemployment rate stayed at 8.2 percent.

Republicans said it showed Obama's policies were not invigorating the economy, while Democrats said it pointed to movement in the right direction.

"Clearly what they're doing is not working," Senate Republican Leader Mitch McConnell told CNN's "State of the Union" program. He called Obama's job creation record "terrible."

"People are unhappy with the economy. They know that Mitt Romney is a job creator," McConnell said.

Gibbs said the employment report showed that the economy was growing. "We've made progress, but we've got a long way to go."

Asked about the Obama campaign trying to define Romney as an outsourcer of jobs in a new ad, Republican National Committee Chairman Reince Priebus responded: "The only job that we need to make sure we outsource in this country is Barack Obama's job."

He said on "Fox News Sunday" that "Barack Obama hasn't done anything in regard to what he promised he would do and making sure that we have a level playing field with China. He's in the sand box with China every day. He hasn't stood up to China."