The battle between President Obama and Mitt Romney reached new levels of rancor Thursday, with each campaign accusing the other of lying over Romney’s tenure at private-equity firm Bain Capital.

The charges flew at a rapid pace, and by the end of the day the Romney campaign was demanding an apology after a senior Obama campaign official said the Republican presidential candidate may have committed a felony.

Obama official Stephanie Cutter made the claim following a Boston Globe article that said documents show Romney was in charge at Bain for three years longer than he had claimed. Cutter said Romney was either misrepresenting his position at Bain to the Securities and Exchange Commission, “which is a felony,” or misrepresenting to the American people.

Romney campaign manager Matt Rhoades issued a blistering statement in response.

“President Obama’s campaign hit a new low today when one of its senior advisers made a reckless and unsubstantiated charge to reporters about Mitt Romney that was so over the top that it calls into question the integrity of their entire campaign,” Rhoades said. “President Obama ought to apologize for the out-of-control behavior of his staff, which demeans the office he holds. Campaigns are supposed to be hard fought, but statements like those made by Stephanie Cutter belittle the process and the candidate on whose behalf she works.”

The challenge capped a frenzied and nasty day on the campaign trail.

Earlier, Romney released a new ad calling Obama dishonest and asking if the American people can “trust him to lead” if he “doesn’t tell the truth.” The release which accompanied the ad in an email to reporters also cited Obama’s “lies and exaggerations.”

The ad titled, “No Evidence,” was an aggressive rebuttal to Obama’s claims that Romney outsourced jobs while at the helm of Bain Capital.

“There was no evidence that Mitt Romney shipped jobs overseas,” a narrator says in the ad.

But the Obama campaign pushed back in a statement charging the ad is part of Romney’s “big Bain lie.”

Relying on the report in the Globe claiming government documents reveal Romney remained CEO of Bain for three years longer than he claimed, the Obama camp statement went on to say the ad is “based on a false premise.”

In a filing with the SEC in February 2001, Bain Capital listed Romney as the company’s “sole shareholder, sole director, chief executive officer and president.” It said Romney’s “principal occupation” was as Bain’s managing director.

Romney’s campaign repeatedly has said Romney had virtually nothing to do with the company’s operations after February 1999, when he began work on the troubled 2002 Winter Olympic Games.

Questions about Romney’s control at Bain from 1999 to 2001 are important in his bid to oust Obama this fall. That’s when the company oversaw investments that either created jobs abroad or filed for bankruptcy. It’s also a time during which Romney stated in federal disclosure forms that he was not active in Bain Capital.

Cutter, Obama’s deputy campaign manager, said Romney may have committed a felony if he misrepresented his role at Bain on the SEC documents. And if he was running Bain after 1999, Cutter said, Romney hasn’t been truthful with the public.

“If that’s the case, if he was lying to the American people, then that’s a real character and trust issue,” she said.

But Romney’s campaign issued a statement Thursday from Bain that said Romney “left Bain Capital in February 1999 to run the Olympics and has had absolutely no involvement with the management or investment activities of the firm or with any of its portfolio companies since the day of his departure. Due to the sudden nature of Mr. Romney’s departure, he 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. Accordingly, Mr. Romney was reported in various capacities on SEC filings during this period.”

J.W. Verrett, an attorney and economics scholar at George Washington University’s Mercatus Center, also told Fox News that the original Globe report appeared to “be confused” about the SEC filings.

He noted they refer to “Bain Capital VI,” which he described as an investment separate from Bain Capital itself.

“Saying that Governor Romney was the CEO of Bain Capital VI is like saying that I am the CEO of my retirement account … it’s a silly bit of legalese and it doesn’t also mean I am CEO of all the companies in which I invest,” he said in an email.

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The Associated Press contributed to this report.