Months after the Sept. 11 attacks, President Bush secretly authorized the National Security Agency to eavesdrop on Americans and others inside the United States to search for evidence of terrorist activity without the court-approved warrants ordinarily required for domestic spying, according to government officials.

Under a presidential order signed in 2002, the intelligence agency has monitored the international telephone calls and international e-mail messages of hundreds, perhaps thousands, of people inside the United States without warrants over the past three years in an effort to track possible “dirty numbers” linked to Al Qaeda, the officials said. The agency, they said, still seeks warrants to monitor entirely domestic communications.

The previously undisclosed decision to permit some eavesdropping inside the country without court approval represents a major shift in American intelligence-gathering practices, particularly for the National Security Agency, whose mission is to spy on communications abroad. As a result, some officials familiar with the continuing operation have questioned whether the surveillance has stretched, if not crossed, constitutional limits on legal searches.

“This is really a sea change,” said a former senior official who specializes in national security law. “It’s almost a mainstay of this country that the N.S.A. only does foreign searches.”

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