Does Kirill die in the Bourne Supremacy?

Answer 1

Presumably he does. In The Bourne Ultimatum Jason Bourne tells Marie Kreutz's brother Martin that he had killed her killer (Kirill).

No. Kirill is left horribly injured, but his eyes are still open and he's still moving, albeit slightly. It contradicts the story for Bourne to kill him without the film elaborating further on it. In the confrontation with Abbott earlier in the film, Bourne says he will not murder out of respect for Marie's values, even if it means letting those responsible for her death live. His statement in Ultimatum that he killed Kirill only makes sense as a lie meant to put her brother's mind at ease.

Answer 2

Yes. Kirill was died because of car accident in Moscow. Kirill's Mercedes Benz G Class Jeep was collided by Jason Bourne's GAZ Volga Taxi Car on wall of underground road.

After that Kirill was died and blood is dripping and Kirill's head was full of blood while Jason Bourne was stay alive.