What is a good alternative to 'I'm sorry I upset you?'

I recently wrote something that upset another person. I had no intention of upsetting them and I felt sorry that I had. I replied to them that I was sorry that I had upset them, that what I had written was not intended to be hurtful, and that I was sorry if it had come across that way (I also went back and made edits to the text to try to avoid upsetting anyone else). I tried to apologise in a way that was genuine and heartfelt but instead of being appeased, the person accused me of giving false apologies and pretending to be nice. I tried a bit more to make things right but nothing I said or did seemed to work. I'd like to ask what could I have done differently? What would you do in this situation?