An alternative to "I'm sorry" is "My condolences"

Dear Miss Manners: I am a reasonably empathetic person. I’m not a sob sister, but I do feel true sympathy for other people’s misfortunes. But I have reached my limit.

If someone tells me that a family member has died, and I respond with an “I'm sorry,” the rejoinder is often, “Not your fault.” If a friend mentions her recently broken bone, her divorce, her speeding ticket or broken fingernail, I obviously say that I am sorry. Again, the response is, “Not your fault.”

I agree that I was not the cause of any of the aforementioned disasters; I was not indicating my guilt. I am certainly old enough to say “You have my sympathy,” but I am not formal enough to pull it off. “I see” seems heartless. “Imagine!” seems cruel. “That is so sad” sounds sarcastic.

In this age of online trolls, rudeness passing as humor, and constant hate speech by politicos, what does one say to show empathy with a friend’s or acquaintance’s tale of woe, discomfort or loss? I need an appropriate response or I’m going to start saying “huh.”

A response that would meet the letter-writer's needs is: "My condolences." 

You can make it more formal or intensive (e.g. "My most heartfelt condolences to you and your family") or just leave it as it is, depending on what's most suitable to the context. 

You can also use "My condolences" as a wry response for things like speeding tickets or broken nails, but if you want a more sincere response, and option is "Oh no!", with the same tone and delivery you'd use if the next thing coming out of your mouth was "I'm so sorry!"

I agree with Miss Manners and with LW that "I'm sorry" is perfectly appropriate, but apparently this standard script leads the people around LW to respond in a way that LW dislikes, so it's time to change up the script. I am surprised that Miss Manners didn't suggest this phrasing in her response.