Sorry IF you were offended
"I can see that you're upset by what I did. I am sorry for that."
"If what I did upsets you then I am sorry."
"If there's anything I did that might have upset you then I am sorry."
Does anyone remember a very funny audio collection of Clinton apologies - He apologized in several languages (including "jive" - where he simply says, "My bad.") It was hilarious.
“Mr. President, it is very clear that even though I thought I had said something that clarified the situation, to many people it was still unclear. I'm sorry if anything that I said caused any offense or pain to those who have such bitter memories of the Holocaust, the greatest moral tragedy of our time. Nothing, nothing should ever be said to demean or diminish that moral tragedy.”
“I'm also sorry if anything I said in any way cast a negative light on our fine men and women in the military. I went to Iraq just a few months ago with Senator Harry Reid and a bipartisan Senate delegation. When you look in the eyes of the soldiers you see your son and daughter. They are the best. I never, ever intended any disrespect for them.”
I have learned from experience that a qualified (using the word "if" is a red flag) apology is no apology.