So is it like the English phrase "I'm fine, thank you" (a polite way of declining an offer)? It's like saying: "I don't want anything, but thank you for offering."
"Would you like some more fish?" "No. I'm fine, thank you."
"Ви хочу більша риба?" "Ні. Дякую, я не хочу."
Does it work like this?