In a letter to the editor about the 1953 coup against Iran, Jonathan Schwarz points out that "no prominent U.S. politician has ever apologized for our role in the coup." Examining a statements made by the Secretary of State admitting that the coup was clearly a setback for Iran's political development," Schwarz quotes Voice of America which accurately reported at the time, "Mrs. Albright did not actually apologize."
I have see other people in addition to Ray Takeyh, a senior fellow at the Council on Foreign Relations, make the claim that the U.S. apologized. For those tempted to suggest that what Albright said was an apology, the question of whether what she said was indeed an apology was put directly to Albright. The same day she made her speech in which she said, "it is easy to see now why many Iranians continue to resent this intervention by America in their internal affairs," a reporter pointed out that she had not apologized for the coup that toppled Mossadeg. Responding to the question, "you didn't come out and say it -- an apology -- but does the United States apologize for supporting the coup against Dr. Mossadegh?", Albright replied flatly, "I said, I think, everything that I needed to say on the Mossadegh coup."