I'm sorry Used for telling someone that you are ashamed or unhappy about something that you have done that has hurt or upset them.
I/we regret to/inform/tell you that Used when you are giving someone bad news.
My (humble/deepest/sincere etc. ) apologies
Used for saying that you are sorry for something.
I beg your pardon
(formal) Used for saying you are sorry because you have made a slight mistake, for example because you have stood on someone's foot. 'Sorry' is a less formal way of saying this.
Excuse me
Used for showing you are sorry for interrupting someone.
Regrettably (adverb)
Used for saying that you are sad or sorry about something.
Forgive me (for doing something)/forgive my doing something
Used when you want to say or do something that may offend the person you are talking to.
I'm afraid
Used for politely telling someone something that might make them sad, disappointed, or angry, for example when you cannot do what they want or do not agree with them.
Due to/for reasons beyond someone's control
Used for saying that you are not responsible for something that has happened, especially when you are sorry about it.
Unfortunately (adverb)
Used for saying that something is sad or disappointing.