Here is what an apology sounds like:
"What I said was incredibly insensitive. I should never have said such a thing. I certainly do not believe it to be true, and I hope you can forgive me."
And then, IF you think you can do so without making things worse, you can try to explain what you really meant.
Here is what an apology does not sound like:
"I'm sorry if you were offended by what I said."
Because, seriously. This is the kind of thing a six-year-old does when ordered to apologize. Mom says, "Billy, you apologize to your sister for calling her stupid."
And Billy says, "I'm sorry you're stupid, sis."
Get it straight. You are in the public eye. Everything you say and do is recorded for all time. And we are watching.