I usually let them live with a city or two for another 15 turns or so while leeching off them. On Deity, after the first archer rush where you kill their warrior horde they'll come at you with maybe chariots and catapults. Nothing you can't handle with your lv2 archers. If they have a medieval unique tho, like Arabia's Mamluks, I wipe them out because they can be hard to finish without losing some of your archers.
EDIT: They won't actually "come" at you, just a saying.