The church, where Jesus is believed to have been crucified, buried and resurrected, is one of Christianity's holiest sites.
The statement, signed by Roman Catholic, Armenian and Greek Orthodox church leaders, also condemned plans by the Israeli government to begin imposing taxes on church properties.
Supporters of the bill say it will limit the church's ability to sell its land to private buyers in order to protect Israelis living on former Church land from not having their leases extended.
"I understand that the Church is being pressured, but their lands remain theirs, no one has any interest in touching them", she said.
Greek Orthodox Patriarch of Jerusalem Theophilos III announced the decision on Sunday alongside Franciscan Custos of the Holy Land Francesco Patton and Armenian Patriarch Nourhan Manougian.
Jerusalem Mayor Nir Barkat has said the city is owed $186 million in uncollected taxes on Church assets. But does it make sense to anyone that commercial areas like hotels, halls, and businesses should be exempt from municipal taxes only because they are owned by churches?
Sheriff: 'Disgruntled student' allegedly overheard threatening to shoot at school
Jacobsen said he thought the student had been arrested, but a sheriff's detective would not confirm whether that had happened as of Tuesday.
At a news conference in front of the church's bolted wooden doors the church leaders said the bill "reminds us all of laws of a similar nature which were enacted against the Jews during a dark period in Europe".
Jerusalem's famous Church of the Holy Sepulchre has shut indefinitely in an unprecedented move amid a fierce row with the Israeli government.
Al-Qawasmi called for a firm worldwide stance against the Israeli measures that contravene all conventions on Christian holy sites in the occupied city. In a statement, they said that Christians in the region were under attack.
Knesset member Rachel Azaria, who proposed the expropriation bill, said that "the low prices at which entire neighborhoods were sold show that it was a speculative deal".
Separately, Christian leaders say legislation being considered by Israel's government would allow church property to be expropriated. They were entrusted to them by Saladin, the Muslim conqueror who seized the holy city from the Crusaders in 1187, which represents the very core of Jerusalem's coexistence between religions.
He pointed out that these steps clearly target the historical Christian presence in Jerusalem, which is an essential part of the Holy City's history and its historical, human, religious and civilizational heritage, and embodies the values of interfaith coexistence in its fullest form.