Is it permissible to say "Have mercy on me" or "Have mercy on us" to people, knowing that some believe it is not permissible to ask for mercy from anyone but God?

There is no harm in a Muslim saying to another: "Have mercy on me" or "Have mercy on so-and-so," because mercy means compassion, gentleness, and tenderness. These are attributes of Allah Almighty with which a servant should adorn himself. Allah has described His Prophet Muhammad, peace and blessings be upon him, with it, and the Prophet encouraged embodying it by saying: "The merciful ones will be shown mercy by the Most Merciful. Be merciful to those on Earth, and the One in the heaven will be merciful to you." Mercy is one of the attributes shared between the Creator and the created.