An arson attack on Thursday gutted part of the church at the site where Christians believe Jesus performed a miracle by feeding 5,000 people with five loaves of bread and two fish on the shore of the Sea of Galilee, the Israeli fire brigade said.

A verse from a Hebrew prayer denouncing the worship of "false gods" was spray painted in red on a church wall, suggesting Jewish zealots were responsible.

"Firefighters arrived at the scene ... and (the fire) was put out, but extensive damage was caused to the church both inside and out," police spokesman Micky Rosenfeld said.

A spokesman for the fire brigade said a preliminary investigation showed the blaze broke out in several places inside the church, evidence that it was started deliberately.

The limestone Church of the Multiplication of the Loaves and Fishes, on the northwest shore of the Sea of Galilee, was constructed in the 1980s and is overseen by the Benedictine Order.

It was built on the site of 4th and 5th century churches that commemorated what Christian faithful revere as Jesus's miraculous feeding of five thousand people with five loaves of bread and two fish.

"The torching of the church is a cowardly and despicable act which contradicts Israel's basic values," Internal Security Minister Gilad Erdan said in a statement.

The Rabbis for Human Rights group said there have been 43 hate crime attacks against churches, mosques and monasteries in Israel and the occupied West Bank and East Jerusalem since 2009.

Dozens of arrests have been made in such cases, but there have been few indictments and convictions, with police and prosecutors acknowledging that the young age of many of the suspected perpetrators has led courts to show leniency.

Desiree Bellars, a volunteer at the church from South Africa who lives at the site, said the blaze erupted in the dead of night.

"All the electricity went out, the fire raged and the flames shot up into the sky," she told Reuters.

No damage was reported to 5th century mosaic floors that have been restored in the church.