Senior Romney adviser Eric Fehrnstrom told MSNBC Romney "disagrees with the court's ruling that the mandate was a tax."
Romney -- who as Massachusetts governor signed a healthcare-reform law in 2006 with an individual mandate that's comparable to the mandate in the Affordable Care Act -- "believes that what we put in place in Massachusetts was a penalty, and he disagrees with the court's ruling that the mandate was a tax," Fehrnstrom said.
"He disagreed with the ruling. He disagreed with the findings of the ruling. He disagreed with the logic that supported those findings. He said that he agreed with the dissent, which was written by Justice [Antonin] Scalia, and the dissent clearly stated that the mandate was not a tax."
Pressed to make clear that Romney believed the levy should be called "a penalty or a fee or a fine" but not a tax, Fehrnstrom said, "That's correct."
David Axelrod, senior adviser to President Barack Obama's re-election campaign, said in an e-mail to The New York Times that Romney could not agree with his fellow Republicans because to do so would be "to condemn himself."
Republican leaders -- led by House Speaker John Boehner, R-Ohio, and Senate Minority Leader Mitch McConnell, R-Ky. -- accused Obama on Sunday morning talk shows of raising taxes on middle-class Americans with the mandate, something Obama promised never to do.
The individual mandate requires all Americans to maintain minimal essential health-insurance coverage or pay a fine, unless exempted for religious beliefs or financial hardship.
Obama argued before the law's 2010 passage that the requirement wasn't a tax, but a way to make sure those with insurance wouldn't have to subsidize the uninsured.
Chief Justice John Roberts said in the court's majority opinion Thursday the mandate could be "reasonably characterized as a tax."
Romney was not available for comment on the matter Monday.
Campaign spokeswoman Amanda Henneberg said the campaign agreed with Fehrnstrom on the mandate, but gave the message a twist.
"The federal individual mandate in Obamacare is either a constitutional tax or an unconstitutional penalty," she said. "Gov. Romney thinks it is an unconstitutional penalty. What is President Obama's position?"
McConnell aide Don Stewart echoed this, saying the White House and Democrats had to decide whether they believe the mandate was "an unconstitutional 'penalty' or ... a constitutional tax as the court ruled.
"It's either unconstitutional, or it is a tax," he said.
White House Chief of Staff Jack Lew told ABC News' "This Week" Sunday: "The court found it constitutional. Frankly, what you call it is not the issue."