His Republican opponent has dismissed the claim as "false."
The US presidential race has taken an acrimonious turn in the past week as the wealthy Republican candidate endures a Democratic onslaught over the Bain issue and for squirreling many of his millions away in offshore tax havens.
Romney, the former governor of Massachusetts, on Friday called for an apology for the intensifying character assassination by the Obama campaign and said personal attacks against him were "beneath the dignity of the presidency".
"We won't be apologising," Obama said, according to the transcript of an interview with a local Virginia TV station airing Sunday.
"Mr Romney claims he's Mr Fix-It for the economy because of his business experience, so I think voters entirely, legitimately want to know what is exactly his business experience."
The manner in which Romney acquired his fortune at the helm of Bain, the Boston-based investment firm he founded, has emerged as a major issue during this campaign as Obama tries to paint him as out of touch with ordinary Americans before the November vote.
Romney maintains he quit the day-to-day running of Bain in February 1999 and was not making the decisions when companies it worked with subsequently laid off US workers and "outsourced" jobs to plants in Mexico and China.
Barrage of attacks
But a Boston Globe report on Thursday revealed that filings with the Securities and Exchange Commission still listed him as Bain's chief executive between 1999 and 2003.
"As the head of a private equity firm his job was to maximise profits and help investors. There is nothing wrong with that," Obama said in his interview with Virginia's WAVY-TV.
"On the other hand that company also was investing in companies that were called by the Washington Post: 'the pioneers of outsourcing'".
The Romney campaign sought to deflect the barrage of attacks on the candidate's business career by framing his departure from Bain Capital as a "patriotic" act to save the Salt Lake City Olympics.
A senior aide to the Republican White House hopeful branded the allegations that Romney oversaw the shipping of US jobs abroad as "baseless" and accused Obama of demeaning his office with such charges.
"He left a life he loved to go to Salt Lake City to save the Olympics for a country he loves more," Ed Gillespie told CNN.
"In classic Chicago-style politics, the Obama campaign is trying to make this something sinister. It's not. It's patriotic and it's leadership."
Romney became president and chief executive of the 2002 Salt Lake City Winter Olympics organising committee and is widely credited with turning the games around, having inherited an event dogged by a corruption scandal.
"It was a 16-hour a day job," said Gillespie. "He was not involved in the management [of Bain after February 2009]. He was not involved in the day-to-day decisions, and wouldn't have had time."
The battle to decide the November 6 presidential election has become increasingly bitter as both sides pepper crucial swing states such as Ohio, Virginia and Florida with a slew of negative TV ads.
An ad released by the Obama campaign on Saturday features Romney's off-key singing of the patriotic anthem America the Beautiful interspersed with clips of Bermuda and the Cayman Islands and scathing attacks about Bain and the candidate's hidden money.
The Romney team has hit back by pointing out that Obama was elected promising to change the tone of American politics and saying his negative strategy is purely designed to obscure his failure to help the US economy.
"No ad is going to decide this election, whether the president likes it or not. The economy and jobs are going to decide this election and his record on that is abysmal," Republican Senator Kelly Ayotte told ABC News.
Obama maintains that with outside groups now pouring tens of millions of dollars into negative ads against him thanks to the "Citizens United" Supreme Court ruling in 2010, he has no choice but to follow suit.
Relentless attacks on Romney's time at Bain are seen as boosting Obama's chances in key swing states.
The largest number of Obama campaign ads have targeted the key rust-belt battleground of Ohio, looming as a must-win state for Romney in November. Obama was due to campaign in the state on Monday. – AFP