In an unusual turn, 5 of the 12 judges issued separate written opinions on the question of whether the plaintiffs had legal grounds to sue the government.

Judge Gerard E. Lynch, explaining why the lawsuit should move ahead, wrote that the case represented an important test of the balance between the government’s ability to detect national security threats and the plaintiffs’ claims to privacy under the Fourth Amendment.

“The Constitution sets limits on the powers even of Congress,” Judge Lynch wrote. “It is the glory of our system that even our elected leaders must defend the legality of their conduct when challenged.”

Chief Judge Dennis G. Jacobs was equally forceful in arguing that the lawsuit should not proceed. He called the suit “frivolous” and likened it to a “plaintiff’s allegation that the C.I.A. is controlling him through a radio embedded in his molar.”

The chief judge wrote that “the only purpose of this litigation is for counsel and plaintiffs to act out their fantasy of persecution, to validate their pretensions to policy expertise, to make themselves consequential rather than marginal, and to raise funds for self-sustaining litigation.”

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The judges were unable to agree on even the basic impact of the 2008 wiretapping law at issue.

The law, known as the FISA Amendments Act, grew out of the disclosure of the Bush administration’s secret operation to wiretap the international communications of people suspected of terrorist ties, without first going through the courts.

With the Bush administration citing national security threats, Congress agreed to put in place a new wiretapping system allowing intelligence officials to make decisions about eavesdropping targets without having to get individual court warrants.

Judge Lynch wrote that the law “indisputably and significantly broadens the risk of interception” for Americans’ communications, lowers the burden of proof for the government in wiretapping suspects and decreases the oversight role of judges.

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But the dissenting judges suggested that the plaintiffs — and the opposing judges — had exaggerated the law’s impact. The statute “makes plain that any surveillance under that statute must be conducted consistent with the Fourth Amendment,” Judge Reena Raggi wrote.

The Justice Department declined to comment. It could still decide to appeal the issue to the Supreme Court, a path that several Second Circuit judges suggested would help resolve the lingering constitutional issues in the case.

But unless the Supreme Court hears an appeal, it will now be up to a federal district court to consider the merits.

“These are issues that have a significant impact on Americans’ privacy rights,” said Jameel Jaffer, a lawyer for the American Civil Liberties Union who handled the case.

“And it’s a very important decision, from our perspective, for an appeals court to say that the courts have a role to play in assessing the constitutionality of a government surveillance program,” he said.