How can I cancel the quest to kill Paarthurnax?

When the blades ask you to kill Paarthurnax (the dragon or the leader of the Greybeards) where are they located so that I can cancel that mission and tell them that I don't want to kill him.
Best Answer
You can't. You have to go confront Paarthurnax to continue the main story. There is no way to cancel this quest.
However, Paarthurnax speaks to you and offers you alternatives to killing him, which you may take him up on.
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Can you do blades quest without killing Paarthurnax?
Edit: After you meet Paarthurnax, you cant join the Blades unless you kill him.Can you kill Paarthurnax after the main quest?
Yeah, you can still kill Paarthurnax after the main quest in completed. In my game it is the only way to make Graybeards appear again, as after the main quest they vanished from the world... Well, just leave Throat of the World and return after few hours.Skyrim: How To avoid killing Paarthurnax
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Answer 2
If you are trying to play through the Blades' storyline without killing Paarthurnax, you simply can't.
It's a choice you need to make in the game. It's like going with the Imperials versus the Stormcloaks. You just have to choose.
Either way, you're not really missing out on much. Both the Greybeards and Esbern will give you locations of word walls. The Blades are a bit more interactive, though (recruiting followers, dragon-killing missions, the like).
If you were on the PC, there is a neat little mod called (aptly) The Paarthurnax Dilemma. This mod would allow you to play both sides of the fence: Paarthurnax can live, but you can still play the Blades questline.
Answer 3
If you try to kill him while he is still essential (while you still need him) get his health down to zero and before his health regenerates fast travel to sky haven temple and it should say that he died
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