The graffiti written in Hebrew on an outside wall of the Dormition Abbey included phrases such as "kill the pagans" and "death to the Christian unbelievers, enemies of Israel", a spokesman for the Catholic Church in the Holy Land said.
Police said the graffiti had been discovered during a patrol and an investigation had been opened.
The Benedictine abbey is located on Mount Zion across from east Jerusalem's Old City and next to the site where Christians believe Jesus's Last Supper occurred.
It was previously hit in 2014, when furniture and wooden crosses were burned.
"This time it amounts to a real call to murder Christians," said church spokesman Wadi Abu Nassar.
Jewish extremists have targeted Palestinians, Christians and even Israeli military property in "price-tag" attacks -- a term that indicates there is a price to be paid for moves against Jewish settlers.
Earlier this month, two Israelis, including a minor, where charged over the 2014 incident at the Dormition Abbey as well as an arson attack at the Church of the Multiplication on the Sea of Galilee.
That church is located where Christians believe Jesus performed the miracle of loaves and fishes.
The most prominent suspected Jewish extremist attack recently was the July firebombing of a Palestinian home in the West Bank that killed a toddler along with his mother and father.
On January 3, an Israeli court charged two suspected Jewish extremists over the firebombing, including the minor accused in the 2014 arson at the Dormition Abbey.
Vatican efforts to negotiate greater rights at the neighbouring Upper Room, where the Last Supper is believed to have occurred, have sparked opposition from nationalist and Orthodox Jews, who revere part of the building as the tomb of King David.
Pope Francis celebrated a mass at the Upper Room during a visit in 2014