Of the films you mention, Le Samourai was first (1967) followed by Army of Shadows (1969), then Le Cercle Rouge (1970), and finally, Un Flic (1972).
Both these men were great directors, in a class with Akira Kurosawa, Fellini, and Coppola, but I would think it was the other way around... Melville influencing Leone. However, I've read nothing to support this idea.
Leone spent years as a film apprentice in Italy, working his way up from writer to assistant to director. Melville decided to be a director after WWII, and bang, he directed. I've read that he liked Hollywood gangster films of the 30s and 40s, and Le Cercle Rouge is one of the all time greats in this genre.
Both directors have their unique ways of patiently using cinema to build mythic quality characters that live their philosophy. Their films are not about personal change but action, and there is a surreal quality about the images in both films. Le Cercle Rouge happens to be my favorite, with the essential Melville actor, Alan Delon, but also an appearance by Yves Montand and the ubiquitous Bourvil, but I love all of Melville's commercial films -- Bob le flambeur, Le Doulos, and Le Deuxieme Souffle in addition to the four listed above.
Philip, thanks for your thoughtful post. It is indeed more likely Leone was influenced by Melville.
I have only seen The Red Circle by Melville, not crazy about it but interested nonetheless. I will be checking out more of his films in the future... There is indeed a surrealistic quality about it that resonates with that of a Leone movie.