But though our prayer for peace is not limited to the human race, that is certainly where we begin. And how urgent at all times, but especially now, is the need for the prayer begging Christ to give peace to this suffering world. Then we have God's response to that threefold prayer for peace. In Slav use, that is said soon after the Little Entrance and the Trisagion. In Greek use and, again, in the Slav, it comes before the Gospel, and repeatedly thereafter.
Peace be with all.
Now what the priest is transmitting is not his own peace. He is speaking at this moment in Christ's name. Not as the world gives, give I unto you. There is a two-way traffic. Our prayer for peace is the one movement, then the responding movement, God's gift of peace.