President Bush has agreed conditionally to a court review of his antiterror eavesdropping operations under a deal that, for the first time, would open an important part of his once-secret surveillance to a constitutional test.

The disclosure of the agreement on Thursday came as the White House sought to end an impasse over a six-month-old dispute with Congress on the National Security Agency’s program. It monitors the international calls and e-mails of Americans when terrorism is suspected.