In a statement, Patrick Toomey, staff attorney with the American Civil Liberties Union, which had represented Amnesty International and the other plaintiffs, hailed the move but criticized the Justice Department’s prior practice.

“We welcome the government’s belated recognition that it must give notice to criminal defendants who it has monitored under the most sweeping surveillance law ever passed by Congress,” Mr. Toomey said. “By withholding notice, the government has avoided judicial review of its dragnet warrantless wiretapping program for five years.”

The Justice Department change traces back to June, when The Times reported that prosecutors in Fort Lauderdale and Chicago had told plaintiffs they did not need to say whether evidence in their cases derived from warrantless wiretapping, in conflict with what the Justice Department had told the Supreme Court.

After reading the article, Mr. Verrilli sought an explanation from the National Security Division, whose lawyers had vetted his briefs and helped him practice for his arguments, according to officials with knowledge of the internal deliberations. It was only then that he learned of the division’s practice of narrowly interpreting its need to notify defendants of evidence “derived from” warrantless wiretapping.

There ensued a wider debate throughout June and July, the officials said. National security prosecutors raised operational concerns: disclosing more to defendants could tip off a foreign target that his communications were being monitored, so intelligence officials might become reluctant to share crucial information that might create problems in a later trial.

Mr. Verrilli was said to have argued that there was no legal basis to conceal from defendants that the evidence derived from legally untested surveillance, preventing them from knowing they had an opportunity to challenge it. Ultimately, his view prevailed and the National Security Division changed its practice going forward, leading to the new filing on Friday in Mr. Muhtorov’s case.

Still, it remains unclear how many other cases — including closed matters in which convicts are already service prison sentences — involved evidence derived from warrantless wiretapping in which the National Security Division did not provide full notice to defendants, nor whether the department will belatedly notify them. Such a notice could lead to efforts to reopen those cases.