Monsignor Fuad Twal issued his plea in a homily he is to deliver at Christmas Eve midnight mass in Bethlehem, the birthplace of Jesus, a copy of which was obtained by AFP.
The service will be attended by Palestinian president Mahmud Abbas and other dignitaries.
Addressing Abbas, he said "we pray for you and for your mission in finding a just and equitable solution to the present conflict, for Palestinian unity, for the peace and prosperity of your country. We ask God to grant you wisdom and courage."
"This painful reality raises numerous questions concerning our future in this country and causes us much worry," added the 73-year-old patriarch.
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But "the answer lies neither in emigration nor in closing in on ourselves. It consists in staying here and in living and dying here," he added, echoing Pope Francis's concerns of a massive exodus of Christians from the Middle East.
"From this Holy Place, we remember all the adversities in our world: from civil wars in Africa to the typhoon in the Philippines, the difficult situation in Egypt and in Iraq, the tragedy playing out in Syria.