Bishop William Shomali was speaking after extremists torched the Church of the Multiplication of the Five Loaves by the Sea of Galilee, famous for its links to Jesus' feeding of the 5000, last week.
Graffiti of a Hebrew prayer was also sprayed on one of its walls outside, saying "idols will be cast out". Police arrested 16 teenagers for questioning, but released them without charge. The culprits have not yet been found.
He told the Christian advocacy group Aid to the Church in Need that "there is a real escalation in the anti-Christian violence", and that "my fear is that these radicals are increasing in number and in the degree of intolerance."
Israel's Prime Minister Benjamin Netanyahu has condemned the recent attack, calling it an attack on all Israelis, not just its Christian minority.
Rabbis for Human Rights, a campaign group in Israel, has said there have been 43 criminal acts against churches, monasteries and other religious sites in the last six years.
Dr Harry Hagopian, a church consultant and international lawyer, told Premier: "As the political situation has stalled and there is less and less of a scope for a peace process between Israelis and Palestinians, the more those attacks [against Christians] have happened, and it is a source of concern for many Palestinians, Christians and Muslims alike.
"They're people who were born there, they're Arab, their culture is Arab, their language is Arabic... so you cannot take them and put them in a balloon and say they're a different issue from the rest of the geopolitics.
"The Holy Land, don't forget, is home for three monotheistic traditions: Judaism, Christianity and Islam. It's that crucible that works together. But the more the political situation gets bad, the more intolerance and radicalisation come in.
"What the competent authorities should do is go after those people who are causing those attacks and punish them to set an example for other people, and to bring a bit more harmony within the country itself."
Listen to Premier's Aaron James speaking to Dr Harry Hagopian here:
You can listen to Dr Harry Hagopian on Middle East North Africa Analysis on Thursday 25th June on Premier Christian Radio.
