A long-running battle over the Securities and Exchange Commission’s policy of muzzling defendants in enforcement cases is gaining new momentum in the courts, thanks to one of the biggest critics of federal regulatory power.

The New Civil Liberties Alliance, a conservative legal group that has been at the forefront in the clash over regulatory reach, is leading a pair of long-shot challenges looking to knock down the SEC’s half-century-old policy of barring most defendants who settle with the agency from speaking out against the charges.

The effort is part of a broader attack by right-wing activists on the so-called administrative state that includes dozens of recent challenges to SEC rules and those of other agencies.

Officially known as the No-Admit-No-Deny rule — or, to critics, the “Gag Rule” — the SEC’s prohibition on defendants openly protesting their cases after settling with the agency has faced years of criticism from activists, billionaires like Mark Cuban and Elon Musk, and even some judges who say they worry that it violates the First Amendment.

“It’s simply an unconstitutional requirement,” said Peggy Little, senior litigation counsel for the New Civil Liberties Alliance, whose backers have included the Charles Koch Foundation. “Can you imagine a statute that was presented to Congress and said, ‘If the government has a case against you and you want to settle, you have to agree that you will never talk about the government’s claims?’ That’s straight out of the USSR.”

The SEC recently rejected the NCLA’s call to change the rule, a decision that was rebuked by a top Republican on the commission. The group says it plans to sue over the decision. Meanwhile, on Thursday, it pressed a panel of judges on the conservative-leaning Fifth Circuit Court of Appeals in New........

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