The "price-tag" acts of violence were apparently carried out by radical Jewish settlers who carry out random acts of violence against the Palestinian population and Israeli security forces, officials said.
It is the second time in less than a year vandals targeted the Valley of the Cross Monastery in Jerusalem, The Jerusalem Post said.
The monastery's exterior walls were painted with "Happy Hanukkah the Maccabees will succeed," and a nearby car with the words "price-tag," and "Jesus is a bastard," the Post said.
The tires of three cars nearby were slashed.
"I forgave them the first time, I will forgive them the second time. I will forgive them the third, fourth, fifth and 75th times. They feel the need to write on the walls. What they need to do is come inside and have coffee with me," the Rev. Claudio Siebenaler, the superior at the monastery, told the Post.
The majority of Israelis support him, he said, adding it is only 1 percent of the population who are responsible for the extremism and hatred.
"This is the second time we've seen such vandalism here and I believe we will find whoever is responsible. The case of the previous incident remains open and I hope today's event will help us find the culprits," Israel Police commander Haim Blumfield told Ynetnews.com.
The incident was the fifth price-tag attack aimed at Christian sites this year, the Post said.
Israeli security authorities are also investigating the torching of a car In a Palestinian village north of Ramallah, Army Radio said. The assailants also spray-painted the words "price-tag" nearby, the radio said.