Final answer:
The most therapeutic approach is to acknowledge the client's anxiety and offer to talk about their feelings, helping them to start managing their stress.
Step-by-step explanation:
When a client is experiencing anxiety due to a family member's serious illness, it's important to provide immediate emotional support in a therapeutic way. The most therapeutic initial nursing comment would be to acknowledge the client's emotional state and offer support by asking, "You seem anxious. Would you like to talk about how you are feeling?" This approach is non-threatening and opens the door for the client to express their feelings, which can be the first step towards managing their stress and anxiety.