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DERRY, N.H. — Jeb Bush said Tuesday that the enhanced interrogation techniques deployed by his brother after Sept. 11 attacks were no longer appropriate, that he hoped the Supreme Court would rule against same-sex marriage, and mocked Hillary Rodham Clinton for passing few laws during her eight years in the Senate.

In an extensive interview with Sean Hannity of Fox News in New Hampshire, Mr. Bush was by turns serious and playful, at one point audibly chuckling at criticism from Donald Trump, who is now running for president.

“Sorry,” Mr. Bush said of his laughter. But he did not seem sorry.

The Fox interview will be broadcast on Tuesday night, but it could be overheard by reporters standing nearby.

Pressed on the same-sex marriage case before the Supreme Court, Mr. Bush said: “I believe in traditional marriage. I hope the Supreme Court rules that way.”

He added that the country should not discriminate against any American based on sexual orientation.

Mr. Bush, a two-term governor of Florida, was in New Hampshire for a town hall-style meeting a day after officially announcing his presidential candidacy in Miami. He repeatedly rebuked Mrs. Clinton, his biggest Democratic rival, in Tuesday’s interview. He called her record in Libya, where terrorists killed the American ambassador, “a complete failure.”

Recounting her legislative accomplishments, Mr. Bush said of his work in Florida, “I put that record up against Hillary Clinton’s any day of the week.”

But he offered words of praise, as well, calling Mrs. Clinton “smart” and “tough.”

Mr. Bush offered brief and sometimes tart descriptions about some of his Republican rivals in the presidential race.

“Real Texan,” he said of Gov. Rick Perry.

“Fighter,” he said of Gov. Scott Walker of Wisconsin.

“Rich guy,” he said of Mr. Trump.