And in August, it surfaced that the N.S.A. was also systematically scanning Americans’ cross-border emails without warrants and saving copies of any messages that contained discussion of a surveillance target. That meant the plaintiffs did not necessarily have to be in contact with an intelligence target for their communications to be intercepted without a warrant.

In November, Mr. Udall, Mr. Wyden and a third Democratic senator, Martin Heinrich of New Mexico, sent a letter to Mr. Verrilli pointing out both discrepancies and expressing concern that they had not been acknowledged or corrected. Mr. Heinrich did not sign the follow-up letter, and a spokeswoman for the senator, Whitney Potter, said he was satisfied with the Justice Department’s response.

In its December letter, the Justice Department argued that its description of the law had been accurate and noted that “based on a recent review” it had adopted a less constrained interpretation of its duty to notify defendants and had changed its practice. It has also defended itself in related court filings.

The department has argued as well that it was appropriate not to tell the court about scanning Americans’ international emails and saving those that discussed targets, because that activity had been classified at the time and was not relevant to the legal question before the court — whether the plaintiffs had standing.

But Mr. Udall and Mr. Wyden argued that the fact that the information was classified at the time did not make it acceptable to mislead the court into believing Americans’ international messages must be to or from a target to be collected without a warrant.

Jameel Jaffer, an American Civil Liberties Union lawyer who argued the case on behalf of the plaintiffs, said that he would have contended that his clients had legal standing based on the “about the target” collection had the government disclosed that the contents of everyone’s international emails were scanned as part of that program.

“What these letters highlight is the extent to which the government was able to take advantage of the fact that the Supreme Court, as much as the American public, was operating in the dark about the scope of the statute and the way the government was using it,” he said.