MANCHESTER, N.H. — Attacks on Mitt Romney by some of his rivals set off outrage within the Republican Party on Tuesday as voters went to the polls and the candidates turned their attention to South Carolina.

Mr. Romney has been under attack for 48 hours over his role at Bain Capital, the investment firm he helped found. Gov. Rick Perry of Texas equated firms like Bain to “vultures,” and Newt Gingrich demanded answers from Mr. Romney about how many jobs were lost on his watch.

Those statement prompted a backlash from other Republicans, much as similar comments were denounced several weeks ago. These critics argue that the attacks on Mr. Romney are attacks on the free-market system and help the Democrats.

“They are also using the language of the liberal left to attack private equity and condemn capitalism in a desperate and, frankly, unsavory attempt to tear down another Republican with tactics akin to those of MoveOn.org,” said Jesse Benton, the campaign manager for Representative Ron Paul of Texas.