Atheists can use this secular condolence letter to express sympathies for a death without using religious sentiments.
Dear {Recipient},
I heard recently about the passing of {the deceased}. I just wanted to let you know that while you are always in my thoughts, you have lingered there for much longer on the event of this death. I know that {the deceased} is not suffering, but I stand by you in living grief. Truly, the world is less rich for having lost {him/her}.
Please, if there is anything I can do or you simply need someone to talk to, give me a call at {phone}. I hope this tragedy can bring us closer together to memorialize the life {the deceased} lived.
Yours truly,
{Sender}