Israeli forces earlier Wednesday also re-occupied two other Palestinian towns, Jenin and Salfit, and surrounded the Jenin refugee camp.
Amid the escalating violence,Israel rejected a U.S. request to allow U.S. envoy Anthony Zinni to travel to Ramallah to meet with Palestinian leader Yasser Arafat, CNN reported Wednesday night.
U.S. ambassador to Israel Daniel Kurtzer made the request for the meeting on Monday, but Israel said it was "too dangerous" for Zinni to travel there, according to CNN. A State Department spokesman would not confirm the report for UPI.
Two Palestinian militants killed Wednesday in the church compound were among 10 people slain in Israel's self-described "uncompromising war," which also has kept Arafat confined to what is left of his Ramallah headquarters.
Palestinians said two members of the militant Al Aqsa Martyrs Brigades, affiliated with Arafat's Fatah faction, were killed in an exchange of fire with Israeli troops in the yard outside the church, which is built above a cave believed to be the manger where Jesus Christ was born.
"The situation at the Church of Nativity as well as three other churches in Bethlehem is very serious, dangerous and frightening," Father Ibrahim Faltas, a priest inside the Church of the Nativity, told United Press International in a telephone interview.
He said Israeli troops continued to encircle the church, where more than 150 people, including monks, nuns, men, women and children were taking shelter. He also said Israeli troops were besieging three other churches in Bethlehem -- Santa Maria, the Syrian Orthodox Church and the Silivian Church. More than 200 people were taking shelter there.
"The Israeli soldiers ... are shooting at the churches and the mosques," he said.
However, Israel Defense Forces Spokesman Brig. Gen. Ron Kitrey told reporters the soldiers have "clear instructions not to shoot at churches and not to shoot at civilians unless they bear arms and use it against us."
Israeli Defense Minister Binyamin Ben-Eliezer told reporters in Jerusalem that he hopes the people inside the churches will come out, and promised that those who are innocent will be freed.
"We have no interest in breaking into any church. We have no interest in harming any holy site," Ben-Eliezer stressed.
Israel has encircled the Church of the Nativity since Tuesday and has reported gunfire from inside, where they claim Palestinian gunmen are hiding. But Faltas said there are only civilians inside.
"The people ... are not armed," he said, adding their food and water supply had run out.
Some inside were wounded and needed "urgent medical aid."
Bethlehem Gov. Mohamed al Madani told UPI from inside the church that 12 people inside were hurt and two had just died. He said the Israeli army refused to allow ambulances inside to take the wounded to hospitals.
Kitrey said ambulances were allowed into some areas, but not where there is very heavy fighting. "It is dangerous to walk there. The IDF is working under very problematic sniper fire there," he added.
U.S. diplomatic security officers managed to evacuate nine American and four British citizens from the area, Palestinian sources said.
Palestinian medical sources said six Palestinians were killed in the northern West Bank refugee camp of Jenin as dozens of Israeli army tanks and armored vehicles reoccupied the town and tried to break into the camp.
Palestinian militants damaged an Israeli armored vehicle and a bulldozer, and clashed with an army unit as they tried to enter the refugee camp, residents said.
Kitrey said a major was killed and two soldiers were wounded in the Jenin refugee camp.
He said Israeli troops were in control of the northern West Bank and were "destroying terror infrastructure" in the towns of Kalkilya and Tul Karem as well as trying to catch militants in four villages.
Meanwhile, Palestinian witnesses said they saw about 20 army personnel carriers heading to the boundary of the Balata refugee camp, adjacent to Nablus.
Palestinian medical sources said at least 16 Palestinians were killed Wednesday in the West Bank and Gaza during the ongoing clashes.
Fighting also broke out on Israel's northern border Wednesday night as Lebanese Hezbollah guerrillas fired mortar bombs and anti-tank rockets at a string of Israeli positions in the Mount Dov and Mount Hermon areas. Kitrey said the army retaliated with artillery and air attacks on "the sources of fire." The strikes prompted a three-hour battle and a late night cabinet meeting on how to react to the escalation.
(Reported by Saud Abu Ramadan in Gaza and Joshua Brilliant in Tel Aviv, Israel)