I am really / genuinely sorry.
lub
I greatly / very much regret that I have caused you so much trouble.
[fml] I owe you an apology / Please accept my humble apology for the wrongful accusation.
I take back all that I said and apologize unreservedly.
[infml] Sorry not to have written earlier.
lub
I'm sorry you've had to wait such a long time for any sign of life.
I must apologize for the delay in replying to your letter / for being so late with these birthday wishes.
[fml] I beg you / I must ask you to forgive / excuse my mistake.
Please excuse my oversight.
[infml] Sorry! It was all a stupid misunderstanding.
[fml] We regret to have to / To our regret we must inform you that we no longer stock this item.
Unfortunately we cannot supply this part separately.

[fml] - formalnie [infml] - nieformalnie