WASHINGTON — Breaking a long silence about a high-profile National Security Agency program that sifts records of Americans’ telephone calls and text messages in search of terrorists, the Trump administration on Thursday acknowledged for the first time that the system has been indefinitely shut down — but asked Congress to extend its legal basis anyway.

In a letter to Congress delivered on Thursday and obtained by The New York Times, the administration urged lawmakers to make permanent the legal authority for the National Security Agency to gain access to logs of Americans’ domestic communications, the USA Freedom Act. The law, enacted after the intelligence contractor Edward J. Snowden revealed the existence of the program in 2013, is set to expire in December, but the Trump administration wants it made permanent.

The unclassified letter, signed on Wednesday by Dan Coats in one of his last acts as the director of National Intelligence, also conceded that the N.S.A. has indefinitely shut down that program after recurring technical difficulties repeatedly caused it to collect more records than it had legal authority to gather. That fact has previously been reported, but the administration had refused to officially confirm its status.

“The National Security Agency has suspended the call detail records program that uses this authority and deleted the call detail records acquired under this authority,” Mr. Coats wrote. “This decision was made after balancing the program’s relative intelligence value, associated costs, and compliance and data integrity concerns caused by the unique complexities of using these company-generated business records for intelligence purposes.”