Jeb Bush on Tuesday sought to arrest a chorus of criticism from Democrats and some conservatives after he told an interviewer that, knowing what history has since shown about intelligence failures, he still would have authorized the 2003 invasion of Iraq.

Calling in to Sean Hannity’s syndicated radio show, Mr. Bush said he had misunderstood a question that one of Mr. Hannity’s Fox News colleagues, Megyn Kelly, had asked him in an interview shown on Sunday and Monday nights.

“I interpreted the question wrong, I guess,” Mr. Bush said. “I was talking about, given what people knew then.”

The attempt at mopping-up was quick, but it did not bring the controversy to an immediate end: When Mr. Hannity asked about the 2003 Iraq invasion again, in yes-or-no fashion, Mr. Bush said he did not know what the answer would have been, saying, “That’s a hypothetical.” Then, he seemed to go out of his way to absolve his brother, former President George W. Bush, who ordered the invasion: “Mistakes were made, as they always are in life,” Mr. Bush said.