心からお悔やみ申し上げます。
衷心からお悔やみ申し上げます.
I apologize from the bottom of my heart.
I extend my sincere condolences to you.
I really don't know how to apologize to you.
I feel sorry for ~.
I am sorry for your loss.
You are in my thoughts and prayers.
I am so sorry to hear about your mother's death.