
The Church of the Multiplication at Tabgha on the shores of the Sea of Galilee is where many Christians believe Jesus fed the 5,000 in the miracle of the five loaves and two fish.
A church adviser blamed Jewish extremists for the incident and police later said they had detained 16 youths from settlements in the occupied West Bank for questioning.
"In an area near the church, 16 youths were detained for investigation in order to check their involvement in the incident before dawn," police spokesperson Luba Samri said in a statement.
She said 10 of those detained were from Yitzhar, which is known as a bastion of extremists and where some residents have been involved in previous hate crimes.
A member of the Roman Catholic Benedictine order, which manages the site, said one of the buildings within the compound was completely destroyed in the blaze but the church itself was not damaged.
Hebrew graffiti was found on another building within the complex, reading "Idols will be cast out" or destroyed, an AFP correspondent reported. The text is part of a common Jewish prayer.
Two people who were in the compound at the time were treated for smoke inhalation, police spokesman Micky Rosenfeld told AFP, saying there was "a strong possibility" the fire was deliberate.
Father Matthias said an external atrium was "totally destroyed" in the blaze.
"The church, thank God, is in good condition," he told AFP. "We're very happy that nothing happened to the church."
Wadie Abu Nasser, an adviser to the Roman Catholic Church in the Holy Land, said the apparent arson attack would reverberate throughout the Christian world.
"Israel's global image will be harmed," he told Israeli public radio.
"When you put one and one together, between the graffiti and the arson, you can reach a conclusion regarding the potential suspects."
Tabgha was subjected to a previous attack in April 2014 in which church officials said a group of religious Jewish teenagers had damaged crosses and attacked clergy.
There has been a long line of attacks on Christian and Muslim holy places in both Israel and the West Bank, in which the perpetrators are believed to have been Jewish extremists.
"I absolutely condemn such acts," deputy foreign minister Tzipi Hotovely said in a statement.
The site is owned by the German Roman Catholic Church, and Berlin's envoy to Israel Andreas Michaelis said he was "shocked" by the incident.
"I strongly condemn this attack and every form of violence" against places of worship or people working in them, he said in a statement.
"Religious institutions must be as well protected in Israel as they are in Germany and Europe."
Israel's Ashkenazi chief rabbi, David Lau, said such incidents "go against Jewish values and human morality."
"I call upon religious leaders to be vigilant lest extremist phenomena erode the respectful relations that exist between the faiths in Israel," he said in a statement.
"The delicate fabric of these relations must be preserved."
In April, vandals smashed gravestones at a Maronite Christian cemetery near Israel's northern border with Lebanon.
That incident prompted Israeli President Reuven Rivlin to meet church leaders and pledge a crackdown on religiously inspired hate crime.
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