Is it permissible to offer condolences to non-Muslims, and if so, what should be said to them?

It is not permissible to offer condolences to a disbeliever by supplicating for mercy and forgiveness for him, because Allah says: {It is not for the Prophet and those who have believed to ask forgiveness for polytheists, even if they were relatives, after it has become clear to them that they are companions of Hellfire} (At-Tawbah: 113). As for participating in the funeral procession of a disbeliever, it is not permissible, and some said it is disliked, except if he was a close relative, then it is permissible. Some also included the wife, neighbor, slave, and freed slave with close relatives.