Manuel Musallam, head of the Roman Catholic community cancelled midnight mass on Christmas eve and said: "The general atmosphere in Gaza is a sad one.
He said Christian children in Gaza are scared.
"The children told me Santa Claus won't come this year because it's too dangerous."
Musallam celebrated evening mass, but called off midnight mass and Christmas day celebrations. Only about 40 people attended the evening service, held at the community's church.
"We used to see Palestinian children killed by Israeli bullets. Now they are killed by Palestinian bullets. How can we celebrate Christmas in such conditions?" h said.
Most Christmas festivities in Gaza have been scaled back to protest against the fighting between Fatah security forces, loyal to Mahmoud Abbas, the president, and forces loyal to the ruling Hamas movement.
Many salaries have also gone unpaid since the US, EU and Israel imposed economic sanctions on the Hamas-led government.
Um Tareq, a Greek Orthodox woman, said: "We do not feel the cheer of Christmas."
Um Tareq's children have lost three classmates, the offspring of a senior intelligence officer, who were shot dead earlier in December.
"My kids are still in shock at what is happening on the ground between the Palestinians," she said. "It was never like that."
Most of Gaza's Christians live in Gaza City, where they own shops and businesses, and attend Sunday mass at two churches. Some of Gaza's best-known doctors, lawyers, jewellers and judges are Christians.
The vast majority are Greek Orthodox, with a small community of 200 Catholics, some of whom are refugees displaced by Israel in the 1948 war.
|Palestinian Scouts take part in a Christmas |
parade in Manger Square, Bethlehem
Gaza Christians rarely drink alcohol and dress in line with Muslim dress codes.
"We are well-respected, well protected and well behaved," one Catholic said.
Gaza's Christians are not associated with Hamas, though some are affiliated with Fatah and Marxist groups.
Members of the community say they have as much religious freedom under Hamas as they had when Fatah was in control of the Palestinian Authority.
In the West Bank meanwhile, religious leaders from the Palestinian Christian and Muslim communities gathered for mass outside the Church of the Nativity in Bethlehem to celebrate the birth of Jesus.
However, only a few hundred Palestinians have been able to attend due to Israeli restrictions on travel, and only a few thousand tourists are expected to visit.
Most Christians believe the Byzantine church marks the place where Jesus was born.
However religious tourism, once the lifeblood of Bethlehem's economy, has fallen sharply since a Palestinian uprising began in 2000.
The average number of foreign visitors per month has fallen to as low as 20,000 people per month from about 100,000 before the uprising.
But Judeh George Morkus, Palestinian tourism minister, said 8,000 to 10,000 visitors were expected over the holiday period, up from 2,000 last year.