LACONIA, N.H. – His credibility under attack throughout the week, Mitt Romney said Friday that he had “no role whatsoever in the management” of a private equity firm after early 1999. He then demanded President Obama apologize for aides who allege otherwise.

“This is simply beneath the dignity of the presidency of the United States,” Romney said in an interview on ABC, one of several he granted to network and cable stations in hopes of extinguishing the controversy.

Romney said after he left the firm that he retained ownership “until we were able to negotiate a departure” from the company he had founded. “I had no role whatsoever in the management of Bain Capital after February of 1999,” he said, adding that officials at the company and independent fact-checkers had said the same thing.

Obama himself had stepped into the controversy a few hours earlier, citing the inconsistencies over the date of Romney’s departure from the firm and allegations that it had invested in firms that outsourced jobs to low-wage nations overseas. Some Security and Exchange Commission documents have surfaced suggesting Romney played an active role through 2002.

Obama said the questions, raised in numerous media reports and highlighted by his own campaign aides, were a legitimate part of the race for the White House.

“Ultimately, I think, Mr. Romney is going to have to answer those questions because if he aspires to being president, one of the things you learn is you’re ultimately responsible for the conduct of your operations,” the president said in an interview with WJLA-TV in Virginia as he campaigned across the battleground state.

Romney said that was “Chicago-style politics at its worst,” and an attempt by the president and his campaign to detract from the persistently sluggish economy and unemployment that has been over 8 percent for more than 40 months.

One Romney aide said earlier in the week that any suggestion that Romney had shipped jobs overseas was a lie, and the campaign has said repeatedly the break with the private equity firm came in 1999.

Yet documents surfaced for the second straight day that seemed to indicate Romney played an active management role in Bain Capital after that date, when he and company officials say he left the firm to become head of the Olympic Games in Salt Lake City.

Beyond raising questions about Romney’s truthfulness, the discrepancy in dates may be important because of accusations that Bain invested in companies that outsourced jobs overseas after 1999.

That, in turn, goes to the core issue of the race for the White House in dreary economic times: Romney’s claim that as a former businessman, he has the ability to create jobs and finally pull the country out of a downturn that has lingered throughout Obama’s term.

Obama spent much of his day challenging Romney over taxes and spending, telling one audience that if Republicans are unwilling to let tax cuts lapse for the wealthiest Americans, they’re “not serious” about reducing the deficit.

Appearing in Hampton Roads, Va., Obama renewed calls to extend Bush-era tax breaks for those earning $250,000 or less while the two sides argue about higher earners, affecting the top 2 percent of Americans. He charged Republicans with balking, and holding middle-class cuts “hostage.”

But for now, the dispute over outsourcing and the timing of Romney’s departure from the firm he created took a central role in the race.

Documents filed with the federal government by Bain Capital conflict with Romney’s statements about when he gave up control of the Boston-based firm.

The filings with the Securities and Exchange Commission place Romney in charge of Bain Capital from 1999 to 2001, the period in which it outsourced jobs and ran companies that fell into bankruptcy.

Separately, Bain Capital issued a statement saying that Romney “remained the sole stockholder for a time while formal ownership was being documented and transferred to the group of partners who took over management of the firm in 1999.”

“Now, my understanding is that Mr. Romney attested to the SEC multiple times that he was the chairman, CEO and president of Bain Capital. And I think most Americans figure if you’re the chairman, CEO and president of a company that you are responsible for what the company does,” Obama said.