Twal arrived at the Strip to visit local Christians who are unable to travel to Bethlehem for Christmas.
Christians make up a minority of about 3,500 people out of Gaza's 1.5 million mostly Muslim population.
"We know that last year had many negative aspects. It had violence, displacement, hunger and pain. We hope the new year will be truly new with more justice, equality and national unity," said Fuad Twal who later led mass in a Gaza city church.
The Islamist group Hamas seized full control of the enclave in 2007. Since then, Egypt and Israel have maintained a blockade on the territory, carefully monitoring the flow of goods and people to and fro.
Israel usually grants special permission to several hundreds of Christian Gazans to leave the Strip and travel to the West Bank for Christmas. Israeli military authorities said similar policy is expected this year.
In the West Bank city of Bethlehem, believed to be the birthplace of Jesus, Christians prayed in the Church of the Nativity.
"Advent" marks the beginning of a festive season in which millions of Christians around the world make their preparations for Christmas.