The Church of the Holy Sepulchre in Jerusalem has warned that it may shut its doors to pilgrims in protest at a dispute with an Israeli water company.
The church, where many Christians believe Jesus was crucified, has had its bank account frozen at the request of Hagihon over an unpaid $2.3m bill.
The dispute has left hundreds of priests, monks and teachers unpaid.
The church has traditionally not been charged for water, but Hagihon says it is owed money for the past 15 years.
According to the Israeli newspaper Maariv, there was a tacit agreement between the Greek Orthodox Patriarchate of Jerusalem - which, along with the Armenian Orthodox Patriarchate and the Roman Catholic Franciscan Custos, is jointly responsible for the Church of the Holy Sepulchre's administration - and a former mayor of the city that the church would be exempt from water bills.
But in 2004, Hagihon sent a demand to the church for 3.7m shekels ($950,000; £590,000). It was backdated to when the company took over the water supply in the late 1990s.
The Patriarchate reportedly believed it was a mistake because Hagihon did not press it to pay. The company is now demanding that the bill, which has risen to 9m shekels ($2.3m; £1.4m) including interest, be settled.
A Hagihon spokesman said Israeli law did not permit any exemptions.
The company had not taken other enforcement steps, such as shutting off the water supply, in order not to disrupt activities at the site, he added.
Father Isidoros Fakitsas, Superior of the Greek Orthodox Patriarchate at the Church of the Holy Sepulchre, told the Associated Press that an agreement had been reached with Hagihon a few weeks ago.
Under the deal, various denominations of the church would pay their monthly bill and the 9m-shekel debt was to be forgotten, he said.
But to his surprise the Patriarchate's bank account was blocked, making it impossible to pay stipends to some 500 priests and monks, 2,000 teachers and the running costs of more than 30 schools.
According to Maariv, other services have also been affected, including telephones, internet and electricity, as well as companies supplying food.
Father Fakitsas said the Patriarchate would be able to function despite the frozen bank account and that it would try to find an alternative if matters became too difficult, such as opening another bank account.
Patriarch Theophilos III wrote a letter to Israel's prime minister and president warning that the "enforcement of this unjustified step undermines the sanctity and offends the sensitivity of the site".
He told Maariv: "If nothing changes we intend to announce... for the first time in centuries, that the Church of the Holy Sepulchre is closed."
The other Christian denominations which jointly manage the church are said to support the Greek Orthodox Patriarchate in its battle.
The Israeli tourism ministry said the issue was between the Patriarchate and the Jerusalem municipality, but that it was trying to mediate between them and hoped that the dispute would be resolved quickly.