WASHINGTON — 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-Qaida, 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.

Nearly a dozen current and former officials, who were granted anonymity because of the classified nature of the program, discussed it with reporters for The New York Times because of their concerns about the operation's legality and oversight.

According to those officials and others, reservations about aspects of the program have also been expressed by Sen. Jay Rockefeller, D-W.Va., who is the vice chairman of the Senate Intelligence Committee, and a judge presiding over a secret court that oversees intelligence matters. Some of the questions about the agency's new powers led the administration to temporarily suspend the operation last year and impose more restrictions, the officials said.

The Bush administration views the operation as necessary so that the agency can move quickly to monitor communications that may disclose threats to this country, the officials said. Defenders of the program say it has been a critical tool in helping disrupt terrorist plots and prevent attacks inside the United States.