The schools have been on strike since the academic year started on September 1, with parents and school officials accusing the government of discrimination in funding their establishments.
The action affects about 33,000 pupils at 47 schools, most of which are run by the Roman Catholic church but also including Protestant and Orthodox institutions.
School officials say they receive only one-third of the subsidies Israel provides equivalent Jewish schools, and that they will stay on strike until their demands are met.
A meeting Wednesday with the director of Prime Minister Benjamin Netanyahu's office, as well as education and finance ministry officials, failed to resolve the dispute.
The schools' leaders said that besides establishing protest tents outside the education ministry, they were "seriously considering" pressing their communities to shut down Israel's Christian holy sites.
"This would be a painful step for Israel, which could affect it economically and tarnish its reputation," spokesman Botrus Mansour, who is also principal of the Baptist school in Nazareth, told AFP.
"Pilgrims who come here and see the sites closed will ask why, and hear about Israel's anti-Christian discrimination," he said.
Signup to our newsletter and follow us on Facebook and Twitter!
Israel is home to some of Christianity's holiest sites.
One is Nazareth's Basilica of the Annunciation, where Christians believe the Virgin Mary was told by the Archangel Gabriel she would give birth to Jesus.
It belongs to the Roman Catholic Church, which is the custodian of most pilgrimage sites in the Holy Land.
Even more famous, in Israeli-annexed east Jerusalem, is what is widely known as the Church of the Holy Sepulchre, built on the sites where most Christian traditions believe Jesus was crucified, buried and rose again.
It is jointly owned by the Catholics, Greek Orthodox and Armenian Orthodox.
The Christians say that their 65 percent state budgeting was cut to 34 percent two years ago before being reduced to its current level of 29 percent.
The state's offer to return the funding to 34 percent, and to allow parents to fund the balance, was rejected by the principals, clergy and parents, who demand the full funding they say Jewish schools get.
The education ministry reiterated its assertion that there was no difference in the funding of the Christian and Jewish schools of recognised, but unofficial status.
It said Wednesday that the Christians had been offered a number of ways to resolve the differences, but rejected them while choosing to close the schools "at the pupils' expense."