A Romanian Orthodox Church in the Musrara neighbourhood of East Jerusalem was the victim of an arson attack on 2 February.
It follows an arson attack on a church in the Garden of Gethsemane in December and anti-Christian graffiti sprayed onto the doors of the Dormition Abbey, a Benedictine community in Jerusalem, last May. The graffiti said "kill the pagans" and "death to the Christian unbelievers, enemies of Israel".
His Beatitude Theophilos III said the latest attack was a sign of "hatred for the Christian religion" by radical groups in Israel.
He condemned the "failure of official authorities" in the city to put a stop to the attacks.
"Their tolerance towards such terrorist acts will definitely lead to more fuelling of the conflict in the Holy City," he said.
The Patriarch is asking the international community to intervene by opening up a dialogue with the Israeli government aimed at putting a stop to the attacks, which he said represented an attempt by extremist groups to "change the mosaic character of the city of Jerusalem by force".
His calls were echoed by Dr Ramzi Khoury, President of the Higher Presidential Committee of Churches Affairs in Palestine, who said that radical groups were "trying to drag the region into a religious conflict" and were acting with "impunity".
Anita Delhaas, Chief Executive of the International Community of the Holy Sepulchre, said that such incidents "only reinforce the idea for many Christians that the Holy Land is an increasingly intolerant place for them to live in and encourages many to permanently leave the region in search of more tolerant societies."
"The international Christian community must come together to present a unified voice in condemning such actions." Ms Delhaas added that such incidents," she said.