Does apologizing entail recognizing being at fault?
Often, in conversation, something like this will happen:
A: I didn't sleep well last night; My dog ran away; or A family member passed away last night.
B: I'm sorry.
A: Why are you sorry? It isn't your fault.
How do you succinctly and conversationally express that you feel sympathetic for the other person's misfortune without inviting the response (or a variation thereof) "It's not your fault"?
The closest I have to that are "My condolences" or "You have my sympathy," but those phrases don't feel particularly conversational.