The executive branch has the authority execute citizens that pose a threat, unilaterally. Deeming someone as a public enemy clearly shows a measure of restraint from that power. Thus it must be legal. Otherwise the executive branch would find themselves in a position where they cannot point out when something has been done to harm the US, but could in fact just kill that person without comment.

https://www.aclu.org/press-releases/obama-administration-cla...