AFP
The attacks drew a strong condemnation from Israeli Prime Minister Benjamin Netanyahu, who expressed "disgust" over the incidents, his office said.
Police spokeswoman Luba Samri said graffiti insulting to Jesus Christ was "sprayed on the gates of the entrance of the Armenian cemetery... and on a monastery belonging to the Greek Orthodox."
Outside the Monastery of the Cross near the Israeli parliament, vandals also slashed the tyres of three cars belonging to staff, and wrote "price tag" and "Happy Hanukkah" the Jewish holiday now being observed by Israelis, an AFP correspondent said.
Father Claudius, the monastery's abbot, said he had noticed the graffiti at 4:30 am (0230 GMT) when he got up to pray.
"This is the seventh time this has happened," he told reporters at the scene, saying that if the vandals had simply knocked on the door he would have invited them in for tea to talk to them about his faith.
A statement from Netanyahu's office said the prime minister had expressed "disgust" over the attacks.
"The Jewish values by which we were raised, and by which we raise our children, firmly reject such actions," he said in the statement.
"Freedom of worship for all religions in Israel will be preserved and we will take legal action against the immoral people who committed these crimes."
"Price tag" is a euphemism for revenge hate crimes by Israeli extremists, which normally target Palestinians and Arabs.
Initially carried out in retaliation for state moves to dismantle unauthorised settler outposts, they have become increasingly unrelated to any specific government measures.
The attacks tend to involve the vandalism or destruction of Palestinian property and have included multiple arson attacks on cars, mosques and olive trees.
Perpetrators are rarely caught.
At first, the attacks were predominantly in the West Bank, but they have expanded over time to include sites inside Israel and in Jerusalem, where a number of Christian sites have been targeted.
Samri said a third apparent "price tag" attack had been reported in the West Bank village of Shukba near Ramallah, in which attackers set fire to a car and sprayed "price tag" and "happy holidays" nearby.
Police were investigating all three incidents, she said.
In Jordan, the custodian of Muslim holy sites in Jerusalem that signed a 1994 peace treaty with Israel, the government denounced the attacks.
"Jordan strongly condemns these acts which provoke Christians and Muslims, and violate human values and international laws," Information Minister and government spokesman Samih Maaytah told state-run Petra news agency.
"The Israeli government is responsible for protecting holy sites and prevents such attacks."