The Franciscan order has asked Israel to allow some of the 200 or so armed Palestinians sheltering in Bethlehem's Church of Nativity to leave unharmed.
The Roman Catholic order in the Holy Land also called for water and electricity to be urgently supplied to its monks inside the complex, which has been blockaded since 2 April.
About 200 armed Palestinians and up to 40 monks and civilians are surrounded The complex is shared by Christian churches which revere it as the reported birthplace of Jesus Christ
Israel, whose army has sealed off the complex in pursuit of suspected militants among the Palestinians, reportedly rejected the appeals immediately.
But the army itself has hinted that a peaceful compromise may be found to the stand-off, in which one man has been killed and three wounded, including a monk.
Reminder from history
"We urgently demand that the Palestinians be allowed to leave the monastery, with guarantees that their lives will be saved, in order to prevent a humanitarian disaster and a futile massacre that will only serve to increase the hatred between the two communities," said Father Giacomo Bini, the head of the Franciscan order.
The Franciscans' spokesman in the Holy Land, Father David, appealed to Israeli Jews for help, reminding them that his order, founded at Assisi in Italy, had once helped Jews fleeing Nazi persecution.
"We remind them of the heroism of the Franciscans, who saved many Jews during the Shoah [Holocaust], taking them in to their friaries, particularly in Assisi," he said.
According to the Vatican news agency Fides, however, the Israeli Government rejected the appeals with the words: "Stop bothering us".
At the same time, an Israeli army spokesman, Brigadier General Ron Kitrey, has said that he hopes for a deal "that would be beneficial to both sides".
Israel's official position remains that any suspected militants inside the church and surrounding monasteries must stand trial in Israel.
Monk wounded
An Armenian monk at the complex was seriously wounded by an Israeli bullet on Wednesday.
An army spokesman admitted responsibility, but stressed that the monk, who is now in hospital in west Jerusalem, had been dressed in civilian clothes and "looked armed".
The Palestinians took shelter at the Church of Nativity site as tanks rolled into Bethlehem in pursuit of militant groups responsible for suicide bombings and other attacks on Israel.
The Vatican has voiced grave concern about the situation, warning Israel to respect the sanctity of religious buildings.
In an exchange of gunfire on Monday, a Palestinian was killed and two Israeli border policemen wounded while a grenade is believed to have sparked a fire which damaged a meeting hall.
Some damage to the site's churches has also been reported.
After Monday's clash, Father David Jaegar accused Israeli soldiers of an "indescribable act of barbarity", but Israel maintains that Palestinian gunmen fired first, wounding its men.