WASHINGTON — The CIA is paying AT&T more than $10 million a year to assist with overseas counterterrorism investigations by exploiting the company’s vast database of phone records, which includes Americans’ international calls, according to government officials.

The cooperation is conducted under a voluntary contract, not under subpoenas or court orders compelling the company to participate, according to the officials. The CIA supplies phone numbers of overseas terrorism suspects, and AT&T searches its database and provides records of calls, the officials said.

The program adds a new dimension to the debate over government spying and the privacy of communications records, which has been focused on National Security Agency (NSA) programs.

Because the CIA is prohibited from spying on the domestic activities of Americans, the agency imposes privacy safeguards on the program, said the officials, speaking on the condition of anonymity.

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Dean Boyd, a spokesman for the CIA, declined to confirm the program. Mark Siegel, an AT&T spokesman, said: “ We do not comment on questions concerning national security.”