Is it permissible to ask for mercy for deceased non-Muslims, such as Christians?

It is not permissible to supplicate for mercy for deceased disbelievers. However, it is permissible to offer condolences to them for their dead, according to the correct opinion. So, if a Muslim offers condolences to a disbeliever for a Muslim, one says: "May Allah perfect your solace and forgive your deceased." If one offers condolences to a disbeliever for a disbeliever, one says: "May Allah compensate you, and may your numbers not decrease." If one offers condolences to a Muslim for a disbeliever, one says: "May Allah magnify your reward and perfect your solace."