I am writing to express my sincerest apology for my recent [actions/words]. My behavior was completely inappropriate and unacceptable, and I understand that it has caused you [hurt/frustration/disappointment].
I understand that I have caused you [emotional distress/damage to our relationship], and I am deeply sorry. I take full responsibility for my actions and I will do my best to make sure that this never happens again.
I want to assure you that I never intended to [hurt/offend/upset] you. I was [unaware of the consequences/not thinking clearly/acting out of anger], and I realize that is no excuse for my behavior.
I am committed to making amends for my actions and I am willing to do whatever it takes to make things right. I am willing to [meet with you/talk on the phone/write a letter] to discuss what I can do to repair the damage I have caused.
I understand that my apology may not be enough to make up for my mistake, but I hope that you can find it in your heart to forgive me. I value our [relationship/friendship] and I want to make sure that it is not damaged beyond repair.
Once again, I am truly sorry for my [actions/words]. I hope that you can find it in your heart to forgive me and I look forward to hearing from you.