Trip Gabriel/The New York Times

In South Carolina Reporting on the candidates and voters in the Palmetto State.

COLUMBIA, S.C. — Amid calls from Republican leaders to back off criticism of Mitt Romney for deals he made at Bain Capital, Newt Gingrich defended the attacks and called on Mr. Romney to provide more details about corporate buyouts that led to bankruptcies.

He accused “extraordinarily wealthy institutions” of bringing pressure on him to rescind the criticism, and said they were telling him, “You’d better shut up.’’

Jim DeMint, South Carolina’s conservative Republican senator and a Tea Party favorite, called on Wednesday for an end to attacks on “free market principles.” Rudolph W. Giuliani, appearing Thursday morning on Fox News, said, “What the hell are you doing, Newt?”

Mr. Gingrich sought to frame the issue as reflective of Mr. Romney’s “judgment” and “decisions,” in particular deals in which workers lost jobs and pensions while Bain investors profited.

“I’ve raised the question, which I think is a totally legitimate question – what about some companies that Bain took over that went bankrupt?’’ Mr. Gingrich asked Greta Van Susteren of Fox on Wednesday night.

Mr. Gingrich is hoping that his anti-Wall Street theme will connect with a deep vein of economic populism in the South, including South Carolina, with its high unemployment and depressed housing market.

Speaking here at a convention of senior citizens, he portrayed the pressure on him to reverse course as coming from the establishment, both on Wall Street and elsewhere.

“I’m not going to back down or be afraid to say we the American people have the right to know, and any candidate for president has an obligation to tell us,’’ he said.

“No one tells the American people they aren’t allowed to learn what is going on in their very own country,’’ he said.

The line drew cheers, but with Mr. Gingrich never mentioning Mr. Romney by name, it was unclear whether his audience was applauding an

anti-Bain message or a general attack on the roots of the financial crisis and the government’s response.

Pat Pope, 80, said that she had been leaning toward Mr. Romney but that after hearing Mr. Gingrich she might switch allegiance.

But she said she was unfamiliar with the criticism of Mr. Romney’s business career. She thought Mr. Gingrich had been referring to the Social Security trust fund, which he had mentioned at the beginning of his speech.

Told about Mr. Gingrich’s Bain critique, Ms. Pope, who voted for Barack Obama on 2008, said, “That concerns me.”