The inquiries and analyst's account underscore how e-mail messages, more so than telephone calls, have proved to be a particularly vexing problem for the agency because of technological difficulties in distinguishing between e-mail messages by foreigners and by Americans. A new law enacted by Congress last year gave the N.S.A. greater legal leeway to collect the private communications of Americans so long as it was done only as the incidental byproduct of investigating individuals "reasonably believed" to be overseas.

James Comey, then the deputy attorney general, and his aides were concerned about the collection of "meta-data" of American e-mail messages, which show broad patterns of e-mail traffic by identifying who is e-mailing whom, current and former officials say. Lawyers at the Justice Department believed that the tracing of e-mail messages appeared to violate federal law.

"The controversy was mostly about that issue," said a former administration official involved in the dispute.