apology (n)

After arguing with her teacher, the girl wrote the teacher an apology.
She wrote a heartfelt apology letter to her friend, expressing her regret for missing the important event and acknowledging the disappointment it had caused.
The public figure issued a formal public apology for the controversial remarks made during the interview, stating that they did not reflect their true beliefs.
Upon realizing the error, he offered a sincere apology to his coworker, along with a small gift as a token of his remorse for the inconvenience.