To whom was the phrase "May God guide you and improve your state" directed?

When a Muslim sneezes, his Muslim brother says to him: "Yarhamukum Allah (May Allah have mercy on you)," and the sneezer replies: "Yahdikum Allah wa yuslihu balakum (May Allah guide you and rectify your state)." This supplication for guidance and rectification of one's state is Islamically prescribed for a Muslim, and there is no impediment to it for a non-Muslim as well, just as the Prophet, peace and blessings be upon him, used to do with the Jews. However, it is not permissible to supplicate for non-Muslims with mercy and forgiveness, but only with guidance and rectification of their state.